million, billion, trillion... then what?

Fraggle Rocker

02-04-04, 11:34 PM

how would you read 6.022 x 10 to the 23rd?? like if it wasn't in scientific notation? PLEASE help. millions?? trillions??Divide the zeroes into groups of threes, as we do typographically with commas. The first group is a thousand. The second is a million. From then on they take the Latin prefixes for two (billion), three (trillion), four (quadrillion) etc. Yes it gets ugly. 10 to the 39 is a duodecillion. I suppose 10 to the 303 is a centillion.

10 to the 23rd is 100 followed by 7 groups of three zeros:

100,000,000,000,000,000,000,000

So the number in question is:

602,200,000,000,000,000,000,000

That would be read:

Six hundred two sextillion, two hundred quintillion.

By the way, as I may have warned earlier, this is the American system. In Europe they count off groups of six zeroes, not three. Their millions and billions can run into the thousands, not just into the hundreds. They would read this number as:

Six hundred two thousand two hundred trillion.

The entire phrase "six hundred two thousand two hundred" is a multiplier of "trillion." A European trillion is 10 to the 18, not 10 to the 12 as in America. We make the sacrifice of running out of pronounceable names for the exponents much earlier, in return for not having potential 12-syllable coefficients in which to get lost.

If you find that confusing, be glad you're not studying in China. They count off the zeroes in groups of four. Their civilization is so old that their language has a one-syllable word for ten thousand: qian.

curioucity

02-04-04, 11:35 PM

Uh yeah..... there's some problem about this I read a long time ago. Between English and American numeric standard, one increase its naming (like from bi to tri) by a factor of 1,000,000, while the other increase it by the factor of only 1,000 (the later must be the American standard judging from the posts here).

Fraggle Rocker

02-07-04, 08:46 AM

In Germany and most non-Anglophone nations, 1,000,000,000 is called "one milliard"; 1,000,000,000,000,000 is "one billiard," etc. I guess if you walk into a bar in Germany and offer to play a game of "billiards," it could take quite a while.

England does not use this terminology, to them 1,000,000,000,000,000,000,000 is simply "one thousand trillion". (See below for their problem with the word "billion," which is why I didn't use billion in this example.)

It appears that both the "American" system and the "European" system were invented in France at about the same time, a few hundred years ago. It's sobering to realize that before then, no one really needed to be able to count to 10**9. (Sorry, I still use Cobol notation.)

What we call the "American" system (billion = million x 1000) is now in use in North America, Holland, and France. What we call the "European" system (billion = million x 1,000,000) is used in all other countries.

With one exception. Because of the influence of the American financial press, the British press now calls 1,000,000,000 "one billion," instead of "one thousand million." But they have not changed their names for the rest of the powers of ten. Once again, the Brits blaze their own trail and it's a lot more crooked and bumpy than anyone else's! Still, wouldn't it be awkward to call George Soros a "billiardaire" or a "thousand-millionaire."

Here are some websites on the subject:

unc.edu/~rowlett/units/large.html

mathforum.org/library/drmath/view/52579.html

antimoon.com

sweet Pentax

02-07-04, 09:00 AM

I guess if you walk into a bar in Germany and offer to play a game of "billiards," it could take quite a while.

haha , no !
the name of the game is "billiard" , the number is called "billiarde" ( the "e" makes a huge difference )

ps : sorry , OT :p

cosmictraveler

02-07-04, 09:48 AM

Teraflop:

A teraflop is a measure of a computer's speed and can be expressed as:
A trillion floating point operations per second
10 to the 12th power floating-point operations per second
2 to the 40th power flops
Today's fastest parallel computing operations are capable of teraflop speeds. Scientists have begun to envision computers operating at petaflop speeds.

Petaflop:

A petaflop is a measure of a computer's processing speed and can be expressed as:
A thousand trillion floating point operations per second (FLOPS)
A thousand teraflops
10 to the 15th power FLOPS
2 to the 50th power FLOPS
Today's fastest parallel computing operations are capable of teraflop speeds. The National Science Foundation, together with NASA and DARPA, has funded eight research projects for envisioning a petaflop computer. Cray says that its X1 supercomputer is "a major milestone en route to Cray's goal of delivering, by 2010, the world's first supercomputer able to sustain petaflops speeds...on a variety of challenging applications." A petaflop computer would actually require a massive number of computers working in parallel on the same problem. Applications might include real-time nuclear magnetic resonance imaging during surgery, computer-based drug design, astrophysical simulation, the modeling of environmental pollution, and the study of long-term climate changes.

Read more about it at:
Cray provides more information about the X1.

More information on the projects can be obtained from the National Science Foundation .

guthrie

02-07-04, 04:18 PM

England does not use this terminology, to them 1,000,000,000,000,000,000,000 is simply "one thousand trillion". (See below for their problem with the word "billion," which is why I didn't use billion in this example.)

What we call the "American" system (billion = million x 1000) is now in use in North America, Holland, and France. What we call the "European" system (billion = million x 1,000,000) is used in all other countries.

With one exception. Because of the influence of the American financial press, the British press now calls 1,000,000,000 "one billion," instead of "one thousand million." But they have not changed their names for the rest of the powers of ten. Once again, the Brits blaze their own trail and it's a lot more crooked and bumpy than anyone else's! Still, wouldn't it be awkward to call George Soros a "billiardaire" or a "thousand-millionaire."

Nope, for once you are wrong. I have never come across anyone or any publication using milliard or billion in the "correct" british usage, in my 5 years at university (science degree) and 3.5 years since in work. Everyone just uses the billion = 10^9, trillion = 10^12, etc.

TruthSeeker

02-09-04, 11:47 AM

The terminology does differ. Use Giga for billion and you won't get it wrong (eg 1 Gyr=1000000000).

Also, in some coutries they write like this:
1,000,000,000 and 0.1

While in others they do the opposite:
1.000.000.000 and 0,1

I came across that when I moved from Brasil to Canada...
Man... was that confusing...? :D

Fraggle Rocker

02-09-04, 06:54 PM

Nope, for once you are wrong. I have never come across anyone or any publication using milliard or billion in the "correct" british usage, in my 5 years at university (science degree) and 3.5 years since in work. Everyone just uses the billion = 10^9, trillion = 10^12, etc.Anglophone countries never used the "milliard" series. In the old days they just stuck with "thousand million" etc. But the rest of the European languages (save French and Dutch) used milliarde or its gramatically compatible equivalent.

Interesting that even the American meaning of trillion and the whole series has finally caught on. I wondered how long England would be able to remain schizophrenic about it. If a billion were 10**9 but a trillion were 10**18, what would the numbers in between be? A thousand billion and a million billion? Must have been awkward.

Some of the websites on which I found this were not entirely current, which means they could be as much as five years old, and their data could be five years further out of date. (Although Doctor Math is generally more hip than that.) Your first-hand experience correlates with that. I'm sure the pressure to normalize with our meaning of "a billion dollars" started building as far back as ten or fifteen years ago, when the list of the world's "billionaires" became too long to memorize.

I certainly remember being warned by my professors forty years ago to be careful of the difference when reading British texts. I think Howard Hughes was the world's only "billionaire" then and I doubt that he was big news in the U.K.

guthrie

02-10-04, 03:18 PM

*cough cough* Britain. (behind hand "england? ohh dear.")
I cant rememebr exactly, and i can only really speak for the UK, but I think the pressure towards billion etc started further back than that. (but im only 26, so...) I think ive seen evidence for it in books several decades old, but i really cant remember where. But yes it is likley more to do with money than anything else. Scientists have been using 10^9 etc for donkeys years.

Vidd

08-21-04, 10:49 AM

Hmm actually I mistated it, I just checked and it is ((10)^10)^100 not (10^100)^(10^100). But irregardless it is supposed to be larger than the number of atoms in the universe and thus it is unwritable in long form base ten.

Aye. My dad once told me that if I wanted to think about a large number, to take the number of different ways that every single particle of matter in the universe could be arranged (...in the universe). I thought once, which would be bigger, that number, or the fabled google plex? Now, most people would stick with the former, but I'm not so sure. I did some calculating recently and if you wrote out the number - that is, a 1 followed by a google 0s - and entered it into enough iPods to carry the whole thing, and then lay the iPods back-to-back-to-back-to-back, they'd overshoot the Andromeda galaxy by a factor of about 200,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000. (2*10^50) (two hundred quindecillion)

Hypercane

08-21-04, 02:22 PM

Here is John Conway and Richard Guy's system for nameing -illion numbers.

x 10^3 x 10^30 x 10^300 x 10^3000 x
0 - - -
1 un (n) deci (nx) centi milli
2 duo (ms) viginti (n) ducenti
3 tre (s) (ns) triginta (ns) trecenti
4 quattuor (ns) quadraginta (ns) quadringenti
5 quinqua (ns) quinquaginta (ns) quingenti
6 se (sx) (n) sexaginta (n) sescenti
7 septe (mn) (n) septuaginta (n) septingenti
8 octo (mx) octoginta (mx) octingenti
9 nove (mn) nonaginta nongenti

Of course, if you want the largest numbers known to man, try researching upon Transfinite Cardinals. :)

Fraggle Rocker

08-22-04, 12:08 AM

I understand the Latin and the Italian just fine. But I don't understand the math. Are you saying that in this system 10^24000 is one octingentillion?

We're already confused enough with the mixture of Latin and Greek prefixes in the metric system. (Greek kilometer vs. Latin millimeter.) And most scientists have a passing familiarity with what they call "scientific" Latin and Greek. I wonder how sanguine they'll b about having to learn Italian numbers as well. Hitting up Hebrew for Aleph sub null was already going over the top for a lot of people.

We have a couple of species of cardinals in the US and even a baseball team by that name, but none of them are transfinite. ^_^

Hypercane

08-22-04, 01:05 AM

Lmao. Transfinite Cardinal Numbers to be specified. ;)

Vidd

08-22-04, 01:22 PM

I've looked up transfinite cardinal numbers before - I don't really see how they're anything other than a more complicated way of expressing ∞. (Is that even considered a number?)

Hypercane

08-22-04, 02:49 PM

I'm not sure, but some people may consider it a number. Its not just a more complicated way of explaining infity, it just starts out complicated because counting and measuring transfinite numbers in relation with other transfinite numbers isnt as easy as 1-10. If you buy the book "Infinity and the Mind" im sure you will get an ensured view of some of the highest numbers in the kingdom of numbers. ;)

Vidd

08-22-04, 03:42 PM

Right, well, what I heard was that since ∞+x (where x is anything other than -∞)=∞, it wasn't technically a number. I wouldn't know though.

My reasoning though is that transfinite cardinals are like "A1 is every even number in existence" "A2 is every odd number in existence..." etc. (I know that's not right but I think that's about the gist of it) And since infinity is infinity is infinity... <shrugs>

Fraggle Rocker

08-22-04, 04:17 PM

I've looked up transfinite cardinal numbers before - I don't really see how they're anything other than a more complicated way of expressing ∞. (Is that even considered a number?)Whether infinity is a number is more a philosophical question than a mathematical one. It participates in many mathematical processes and it is even the solution to many equations. Still, that doesn't necessarily qualify it as a "number."

There isn't just one infinity, there is a whole hierarchy of them. The Aleph sub null that I spoke of is one of them. Presumably then, there ought to also be Aleph sub 1, sub 2, etc., or why bother with the subscript in the first place.

I'm way over my head already, I stopped studying math when I couldn't see either the joy or the usefulness of being able to solve a partial differential equation.

John Connellan

08-23-04, 04:32 AM

If the number were written out it might extend from one end of the universe to the other. Pretty trippy, huh?

No, it cannot be written out because there is not enough atoms!

slotty

08-23-04, 01:02 PM

Facial

08-23-04, 04:08 PM

Fraggle Rocker

08-23-04, 06:14 PM

It says in the Guiness Book of Records that the largest lexicographically accepted number is the centillion, I think it was 10^600 or something like that.

10^100 is known as a google.

Someone mentioned on the first page "hexillion." I've only heard of sextillion and septillions, but not the hex's and the hep's.In the American system the Latin number n is used as a prefix to mean 10^(3(n+1)). Bis, "twice," in "billion" means 10^(3(2+1)) = 10^9 = 1,000,000,000. So a centillion would be 10^(3(100+1)) = 10^303.

In the English system it would indeed be 10^600.

You're right that the Latin (ordinal) numbers are used for prefixes, not the Greek. Quadrillion, quintillion, sextillion, septillion -- not tetrillion, pentillion, hexillion, heptillion. The exception would seem to be million, which seems to be formed from Greek mono- instead of Latin uni-. However, million was invented by the Romans themselves before anyone ever thought of a number a thousand times larger. It's just mille, one thousand, with the augmentative suffix -on, which is still used in the modern Romance languages. Italian calzone, shoe; Spanish raton, rat.

Dreamwalker

08-23-04, 06:18 PM

Well, I grew up with the sytem containing Milliard (10^9) and Billiard and so on. But thanks to the Americans, Billion is used for Milliard sometimes, mostly in english speaking countries. But many countries still use Million->Milliard->Billion->Billiard....

Hypercane

08-24-04, 02:49 PM

I think the highest -illion number you could name, well according to Conway and Guy's system, Millillion which is 10^3003.

GuessWho

08-24-04, 03:18 PM

Actually one Billion is a disputed sum.

It seems most of the world has one Billion as:

1,000,000,000,000

But I think (correct me If I'm wrong) America has it down as:

1,000,000,000

Thats why when I saw $50 Billion worth of bonds it wasn't worth any more than £35 Thousand Million's (which is are also called Billion's)

So an English Billionaire is actually richer than his American counterpart even if they have the same number of differnt billions.
This is interesting. I did not know that the world's Billion is 1000 greater than the US's Billion.

However, this makes it impossible to be an English billionare unless there is actually someone who has almost 20 times more money than Bill Gates. Last time I check the richest person on earth was Ingva Camprad who has $53,000,000,000 in wealth.

Fraggle Rocker

08-24-04, 06:01 PM

So do the people who don't use the American system call Warren Buffett a milliardaire?

Dreamwalker

08-24-04, 06:05 PM

Yes they do.

(I have to say that the American system got me quite irritated the first time I stumbled across it and noticed that they described those amount another way.)

yuri_395

02-07-05, 11:47 PM

Aye. My dad once told me that if I wanted to think about a large number, to take the number of different ways that every single particle of matter in the universe could be arranged (...in the universe). I thought once, which would be bigger, that number, or the fabled google plex? Now, most people would stick with the former, but I'm not so sure. I did some calculating recently and if you wrote out the number - that is, a 1 followed by a google 0s - and entered it into enough iPods to carry the whole thing, and then lay the iPods back-to-back-to-back-to-back, they'd overshoot the Andromeda galaxy by a factor of about 200,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000. (2*10^50) (two hundred quindecillion)
ya my dad dosen' belive that it passes the andromeda galaxy

Communist Hamster

02-08-05, 01:46 AM

Neildo

02-08-05, 05:13 AM

Yeah, my favorite part was that there's a number so large that it cannot be written down due to not enough atoms being available in the universe to do so, heh.

I also had to recheck the thread to see how many people fit the criteria for Award #2 and found that amusing, lol.

- N

yuri_395

02-09-05, 12:43 AM

I came back! :D

Communist Hamster

02-09-05, 01:50 AM

You're an alternate account of an already existing, high post SF user aren't you? You made that account just to ressurrect the thread without getting told off!

Neildo

02-09-05, 07:41 AM

Roflmao, too funny, heh.

- N

yuri_395

02-09-05, 06:26 PM

but I didn't ressurect the thread :bugeye:

night

09-25-05, 03:05 PM

Hey,
Ten to the 26th = 100,000,000,000,000,000,000,000,000

What would be the scientific name for that?
All i have seen is
"24 septillion quadrillion
27 octillion 1000 quadrillion"

would it be 500 quadrillion?

-Night

Fraggle Rocker

09-25-05, 04:14 PM

In the U.S. it's one hundred septillion.

In most of the rest of the world it's one hundred quadrillion.

If you had chosen 10^29, the answer would show the superiority of our way.

In the U.S., 10^29 is one hundred octillion.

In the countries using the other system, it's one hundred thousand quadrillion.

Pity the Spanish-speaking peoples. "Million" and the larger figures are all nouns and have to be used grammatically correctly. For them "10^29 dollars" is "a hundred thousand quadrillions of dollars," "ciento mil cuadrillones de dólares."

weed_eater_guy

09-25-05, 04:22 PM

i ran this through mathematica and damn-near set my laptop on fire...

how many zeros are in "1000000!"? It must have made hundreds of pages of numbers on my screen show up...

Communist Hamster

09-26-05, 01:54 AM

I give this thread several awards

Award 1 : Most Uses of the number 0 in Non-Spam Messages

Award 2: Mosts Posts by Users who just Registered but then Didn't Come Back
(so they only have 1 post each)

Award 3: Most resurrections.
This thread has been ressurrected over 3 times! And every time it was ressurrected, people payed some attention to it! Now thats gotta deserve a medal of some sort. Some photoshop one up, will ya?

Hey,
Ten to the 26th = 100,000,000,000,000,000,000,000,000

What would be the scientific name for that?
All i have seen is
"24 septillion quadrillion
27 octillion 1000 quadrillion"

would it be 500 quadrillion?

-Night

Oh dear, oh dear, oh dear. It's happened again.

Fraggle Rocker

09-26-05, 05:31 PM

I don't even understand Weed Eater's comment. There are six zeros in 1000000 and it doesn't take any automated tools to figure it out.

jackamo

09-27-05, 09:16 AM

The path of the righteous man is beset on all sides by the inequities of the selfish and the tyranny of evil men. Blessed is he who, in the name of charity and good will, shepherds the weak through the valley of the darkness. For he is truly his brother's keeper and the finder of lost children. And I will strike down upon thee with great vengeance and furious anger those who attempt to poison and destroy my brothers. And you will know I am the Lord when I lay my vengeance upon you." I been sayin' that shit for years.

Solve

09-27-05, 09:18 AM

I'll eat your head, and suck all your blood out you billy goat you.

weed_eater_guy

09-27-05, 09:16 PM

it's 1000000!, as in 1000000 factorial (1 x 2 x 3 x 4 x ...... 1000000)

Hapsburg

09-27-05, 09:41 PM

What comes after trillion? Then after that...?
quadrillion, quintillion, sextillion, septillion, octillion, whatever the fuck "9" is in latein -illion, decatillion, and I forget what's next...
but, eventually, it works its way to 'google", then something else, then "infinity", then "aleph-one".

Fraggle Rocker

09-27-05, 11:19 PM

it's 1000000!, as in 1000000 factorial (1 x 2 x 3 x 4 x ...... 1000000)Oh I see, sorry. Missed the exclamation point in that font. That would be a really big number all right. By inspection it's obviously greater than one thousand to the one thousandth power, which means it will have more than three thousand zeros.

After octillion comes nonillion, decillion, undecillion, duodecillion.

I've seen charts showing what comes next for lots more zeros, but this is what they call "Modern Latin" as opposed to "real" Latin, meaning that it's being invented on the spot. Up to duodecillion, there's a consensus among scientists and mathematicians. Beyond that the laws of Latin grammar are not unambiguous enough that there's more than one logical way to coin some of the terms. They're not in wide enough use for there to be a general agreement.

Obviously everyone will agree that 10^303 is one centillion. But what's 10^54? I've seen both "septemdecillion" and "septdecillion," the latter of which is pretty hard to pronounce.

Pete

09-28-05, 08:21 PM

Oh I see, sorry. Missed the exclamation point in that font. That would be a really big number all right. By inspection it's obviously greater than one thousand to the one thousandth power, which means it will have more than three thousand zeros.
What the hell happened to my post??? I'll try again!

It's easy to show by pairing high and low numbers that a million factorial is greater than a million to the half-millionth power, so it's at more than 3 million digits long.

It's also obvious that it's less that a million to the millionth power, so it's less than 6 million digits long.

As far as actual trailing zeros go, I think that it will end in exactly 249,998 zeros, as that's the number of multiples of 5 and its powers that are less than a million (ie there are 200000 multiples of 5, 40000 multiples of 25, 8000 multiples of 125, and so on).

abyssoft

09-30-05, 10:49 PM

valich

10-06-05, 09:46 PM

Whether infinity is a number is more a philosophical question than a mathematical one. It participates in many mathematical processes and it is even the solution to many equations. Still, that doesn't necessarily qualify it as a "number."

There isn't just one infinity, there is a whole hierarchy of them. The Aleph sub null that I spoke of is one of them. Presumably then, there ought to also be Aleph sub 1, sub 2, etc.,

Yeh but infinity is where this thread is leading to. Where else can it end. How can there be a "hierarchy" of infinities. I don't understand that one. My math stopped at differential equations too.

Hapsburg

10-08-05, 11:13 PM

Myriadaplex is Googolplex^Googolplex
I wanna have that much money. :D

Bridgett_largo

11-03-05, 09:03 PM

well then why were earlier posts putting a sort of "cap" on the number of atoms in the universe at a googolplex? we dont even know about how many atoms are in our planet let alone the universe of which we dont even know a millionth about? ... and yes that much money would be nice XD

Fraggle Rocker

11-03-05, 10:51 PM

Because:

Assuming that our model of the universe is correct and that it has been expanding at the rate we've measured for the time we've inferred...

1. We know what the maximum volume of the universe can be.
2. We know what the smallest possible volume is that an atom can be squeezed into.
3. Therefore, we know what the maximum number of atoms is that can fit into the universe, if they were squeezed as tightly as possible, given the observed conditions of the universe which do not have them packed like sardines.
4. That number is less than a googolplex.
5. Even if we hypothesized that we could pack them as tightly as sardines, we could write a much larger number that would do the job.

And yes, we do have a pretty good idea how many atoms there are in our planet. Certainly the order of magnitude.

When I say "we" I'm not speaking personally because I'm not a physicist. I don't keep that data on file because situations like this rarely come up where I wish I had it; and I don't have the skills to derive it myself. But the scientific community has it. I'm sure someone will pop up on this thread with those numbers, although it might be a year from now because this thread has a very strange habit of going dark for months at a time and then erupting into a flurry of activity.

The point that needs to be brought home here is this: We have a notational system that allows us to very easily and compactly express numbers that are SO LARGE that they have absolutely no practical application.

When you start using multiple levels of exponentiation, it's easy to get into inconceivably large numbers before you know it. If what you read was wrong and the universe really could hold one googolplex atoms, then we can just write a number so much larger that the concept of "orders of magnitude" isn't of any use in understanding it. How about googolplex^(googolplex^googolplex)?

The calculations I outlined above in the first three steps are trivial. I actually could track down the source data and do the arithmetic, without having to be a physicist. It's that easy. We will end up with a number that is expressed with multiple levels of exponentiation. It will be either greater than or less than a googolplex. If it's greater, we can write an adequately larger number with just a few keystrokes.

Our ability to express large numbers is expanding faster than the universe. :)

Communist Hamster

11-04-05, 01:38 AM

Pete

11-04-05, 04:17 AM

Perhaps it's the same poster, returning under a new handle every once in a while to revive their favourite thread?

Communist Hamster

11-04-05, 10:42 AM

Perhaps. They should try and remember their password this time.

Bridgett_largo

11-08-05, 06:43 PM

no no its not who ever your thinking of...I actually came across this thred looking for what came after a million, quite helpful really...and thank you I didn't know that we even had a small idea of how big (or small) our universe was, I'm just a highschool student, so alot of this is new to me. Thank you for your help though :D

Pete

11-09-05, 04:26 AM

Thanks for popping in Bridgett!

May I ask how you foud the thread? Was it a search on Google or similar? What keywords did you use?

Thanks, Pete

Fraggle Rocker

11-09-05, 05:12 PM

I also discovered SciForums with a search engine (probably DogPile) three years ago. I just typed in a rather arcane word that only pops up in discussions of linguistics, and a SciForums thread was one of the hits on the first screen.

Communist Hamster

11-10-05, 02:00 AM

I discovered sciforums via Ask Jeeves 3 years ago, looking for something about space. If I remember correctly I found a thread on space warships.

Phade

05-19-06, 02:43 PM

Someone post the answer to Frag's statement about how many atoms are in the universe. I am neither a scientist nor mathematician it’s that I have read all 5 pages and am very interested in this discussion continuing.

And no I’m not the original poster I found this forum by typing (“what comes after trillion”) on the google site. It was the 3rd one down on the page. But, this forum is a very fun read and I think Frag should be writing books on the subject you are very understandable to the people that really don’t have any idea what mathematics are about but are interested.
:D

edit: I did work up a medal for ya but I'm not really all that webucated so I don't know how to post it. :mad:

Walter L. Wagner

05-19-06, 03:02 PM

Valich:

There is indeed a hierarchy of infinities, and it likely plays in physics in ways not yet contemplated.

To evidence two such infinities, consider the counting-numbers (0, 1, 2, 3, 4 ... infinity). They may be paired one-to-one with some of the first few real-numbers (0, 1/1, 1/2, 1/3/, 1/4), before we even get beyond the number 1. Thus the infinity of the real-numbers is a greater infinity than the infinity of the counting-numbers.

Ben Hong, a mathematician, took first honors at the then-annual Cal Poly mathematics contest in 1967 for high school students (at age 17), giving a discourse on such infinities. I believe Scientific American also had an article about that in the 1960s.

Walter L. Wagner (Dr.)

przyk

05-19-06, 03:55 PM

Georg Cantor was the first to prove that if you had an infinite set, you could make an even "bigger" infinite set by taking all the subsets of your original infinite set. I think the proof is a rather amusing one (see: Cantor's theorem. (http://en.wikipedia.org/wiki/Cantor%27s_theorem)). It was a while before Cantor himself was taken seriously by other mathematicians, and I think he even spent time in a mental institution as a result.

Fraggle Rocker

05-19-06, 05:18 PM

Georg Cantor was the first to prove that if you had an infinite set, you could make an even "bigger" infinite set by taking all the subsets of your original infinite set.That's when they started naming the infinite sets. I recall the taxonomy but not how it worked. Aleph-null was the first one. I'm not going to mess around with a character set I probably don't even have. It's aleph sub zero. Aleph is the first letter of the Hebrew alphabet, chosen, I suppose, because the Greek alphabet has been exploited to death and he envisioned a lot of new infinities needing names.

I wonder whether any of this has been re-thought since the advent of fractals. It seems that perhaps they make it easier to map infinities onto each other.

Fraggle Rocker

05-19-06, 05:23 PM

I think Frag should be writing books on the subject you are very understandable to the people that really don’t have any idea what mathematics are about but are interested.I've had the experience of writing part of a book--not even the whole thing--just once. It is nothing like the fun of writing for you folks. It ends up being ninety percent everything else and only ten percent what you really wanted to do. Sort of like playing paying gigs instead of in a garage band. Still, I would probably do it if the financial lure were sufficient, but I don't know how to make that connection.I did work up a medal for ya but I'm not really all that webucated so I don't know how to post it.That's okay, I appreciate your kind remarks just fine.

Pete

05-22-06, 07:58 PM

I give this thread several awards

Award 1 : Most Uses of the number 0 in Non-Spam Messages

Award 2: Mosts Posts by Users who just Registered but then Didn't Come Back
(so they only have 1 post each)

Award 3: Most resurrections.
This thread has been ressurrected over 3 times! And every time it was ressurrected, people payed some attention to it! Now thats gotta deserve a medal of some sort. Some photoshop one up, will ya?
What is it with this thread?
I think that's six bumps by new users (and counting)?

CANGAS

05-22-06, 10:41 PM

On the extremely rare occaision that my number is so big that I'm too lazy to calculate it, I call it a Gillian.

Absane

05-25-06, 01:59 AM

Yeh but infinity is where this thread is leading to. Where else can it end. How can there be a "hierarchy" of infinities. I don't understand that one. My math stopped at differential equations too.

There are ways to "number" numbers. If you can create a function that maps the natural numbers N ( N = {1, 2, 3, 4, ...}) to an infinite set that is onto, then the set is called infinitly countable. all integers are countable, the subset of integers of even numbers is countable. All the rational numbers are countable (1, 1/2, 43/2232, -23, ...). However when you try to count irrational numbers, you cannot. Real numbers include both rational and irrational numbers... we know that the rationals are countable but not the rational... so we can see there is another "kind" of infinity. Pretty much this new infinity is bigger than the previous infinity. LOL.

By the way, BUMP!

s0meguy

05-25-06, 02:58 AM

"It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired."

http://www-users.cs.york.ac.uk/~susan/cyc/g/googol.htm

:D

Absane

05-25-06, 03:21 AM

Then a googolplex for me would be about 1,000,000. I hate writing numbers, even though I am a math major. Then again, I deal with x and y :D

Fraggle Rocker

05-25-06, 07:55 AM

But what is the basis for stating that a set of numbers that is infinitely countable is "smaller" than one that is not? Our system of defining numbers as the ratio of two integers does, after all, apply to irrational numbers. Rational numbers are merely a special case in which the numerator and denominator do not have to approach infinity. This strikes me as being an artifact of the particular kind of mathematics we have developed over the past 2,500 years. Square roots are just as easy and compact as ratios to define in our notational system. So are the solutions to any exponentiation which can be described with integers. And therefore, so are the solutions to any second-order exponentiation that can be described with the solutions to first-order exponentiations.

The set of all numbers of the form A ^ (B/C), where A, B, and C are integers, is just as countable as the set of all numbers of the form B/C. The mapping of a space of three or any arbitrary number of dimensions onto a two- or one-dimensional space is trivial.

By reiteration, the set of all numbers of the form D ^ (E/F), where D, E, and F are of the form set forth above, is just as countable.

It would seem that the solution to any formula that we can express using integers must be as countable as the integers. This includes trigonometric, logarithmic, and hyperbolic formulas.

We could end up mapping a space with an infinite number of dimensions onto a one-dimensional space, which is merely another way of saying that the space has an additional infinite dimension. Do two dimensions of infinity make a set of numbers "larger" than one? Is there a precedent for this?

Our ability to express irrational numbers compactly is only limited by the formulas we have discovered to date. We cannot assume that this set of formulas is not infinite. Will it, therefore, encompass all numbers so that there is only one infinity?

Absane

05-25-06, 08:34 AM

Fraggle...

The reason rational numbers are countable is because, roughly speaking, there exists a way to list them in a set that includes all rational numbers. Irration numbers are not countable because there does not exist a way to list them in a set (when one thinks they listed all the irrational numbers, you can always create a new one).

How is A^(B/C) countable if you let B/C = 1/2 and K = {A^(1/2) : A is in [0,1]}? It includes an infinite number of irrational numbers and A is not even countable.

Aleph-0 is any set having the same cardinality as the set of integers, like rational numbers... Let Aleph-0 = X

XX = c, which c is the nondenumerable set of real numbers, called the continuum. Also, X + c = c.

Giambattista

05-25-06, 10:22 AM

And for 3 more insainly large numbers

Myriad is Googol^Googol
Myriadol is Googol^Googolplex
Myriadaplex is Googolplex^Googolplex

I remember my Calc prof telling my class about these and said that these have no real practical value.

Complete BS. I use these all the time. In fact, none of us would be here if it weren't for myriadaplex. :(

Fraggle Rocker

05-25-06, 11:08 AM

The reason rational numbers are countable is because, roughly speaking, there exists a way to list them in a set that includes all rational numbers. Irrational numbers are not countable because there does not exist a way to list them in a set (when one thinks they listed all the irrational numbers, you can always create a new one).I understand this argument but it seems unproveable. I have demonstrated that rationality is a sufficient but not necessary condition for countability. Based upon history, each time we expand mathematics we stand a good chance in the process of developing a way to list a new set of irrational numbers that includes one or more of the sets already covered. Therefore we cannot say that the possibility does not exist that we will discover a way to list all numbers.How is A^(B/C) countable if you let B/C = 1/2 and K = {A^(1/2) : A is in [0,1]}? It includes an infinite number of irrational numbers and A is not even countable. Aleph-0 is any set having the same cardinality as the set of integers, like rational numbers... Let Aleph-0 = X

XX = c, which c is the nondenumerable set of real numbers, called the continuum. Also, X + c = c.Isn't any set of numbers defined by a function of A, B, and C countable if A, B, and C are countable?

That certainly seems to be the thesis upon which the countability of rational numbers is based: All numbers of the form A/B are countable so long as A and B are integers.

So I count

1 ^ (1/1)/; 1 ^ (1/2); 1 ^ (2/1); 1 ^ (2/2); 2 ^ (1/1); 2 ^ (1/2); 2 ^ (2/1); 2 ^ (2/2);

1 ^ (1/3); 1 ^ (2/3); 2 ^ (1/3); 2 ^ (2/3); 1 ^ (3/2). . . .

or any other way of mapping three variables onto a one-dimensional vector. I get all their values and this particular mapping allows them all to approach infinity at the same decreasing rate.

A ^ (B/C) is indeed countable so long as A, B, and C are integers.

Absane

05-25-06, 11:27 AM

I understand this argument but it seems unproveable. I have demonstrated that rationality is a sufficient but not necessary condition for countability. Based upon history, each time we expand mathematics we stand a good chance in the process of developing a way to list a new set of irrational numbers that includes one or more of the sets already covered. Therefore we cannot say that the possibility does not exist that we will discover a way to list all numbers.

I refer you to a page that might convince you: here (http://mathforum.org/library/drmath/view/52830.html) .

Isn't any set of numbers defined by a function of A, B, and C countable if A, B, and C are countable?

Yes. But then again, this IS the counting function! If A is a subset (may or may not be proper) of rational numbers, then given F:A->B that is onto, then B is countable.

That certainly seems to be the thesis upon which the countability of rational numbers is based: All numbers of the form A/B are countable so long as A and B are integers.

So I count

1 ^ (1/1)/; 1 ^ (1/2); 1 ^ (2/1); 1 ^ (2/2); 2 ^ (1/1); 2 ^ (1/2); 2 ^ (2/1); 2 ^ (2/2);

1 ^ (1/3); 1 ^ (2/3); 2 ^ (1/3); 2 ^ (2/3); 1 ^ (3/2). . . .

or any other way of mapping three variables onto a one-dimensional vector. I get all their values and this particular mapping allows them all to approach infinity at the same decreasing rate.

But your list is only a proper subset of the positive reals. Tell me when A^(B/C) = Pi or e or Euler's Constant.

A ^ (B/C) is indeed countable so long as A, B, and C are integers.

As I said before, this is true. Because you can list these numbers. Yes, irrationals are included in the list but not all of them, just a proper subset of them.

Edit: sorry.. what I actually said was "How is A^(B/C) countable if you let B/C = 1/2 and K = {A^(1/2) : A is in [0,1]}? It includes an infinite number of irrational numbers and A is not even countable."

I never did actually confirm your statement as true, but it is.

Absane

05-25-06, 11:30 AM

Complete BS. I use these all the time. In fact, none of us would be here if it weren't for myriadaplex. :(

myriadaplex? wtf? Google tells me nothing. LIES!

Fraggle Rocker

05-25-06, 12:16 PM

But your list is only a proper subset of the positive reals. Tell me when A^(B/C) = Pi or e or Euler's Constant.I understand that "to count" by definition is the ordination of integers. Therefore we can only count numbers that can be expressed as formulas that are combinations of cardinal numbers. I do indeed intend to play by those rules.

Pi cannot be expressed by my formula or any other that we know of... yet. That does not mean that we won't discover it some day, which is my point.

I'm not familiar with Euler's constant but apparently it can be expressed as an infinite series of simple rational numbers. Unfortunately the people who named e did not foresee Google so it's a little difficult to research, but if memory serves me there is also an infinite series for that one. The ordination of infinite series is not so much a mathematical problem as a lexicographic one. If we can sort all infinite series by their alphanumeric text, that seems like a promising first step toward countability.

I realize that this leaves a lot of irrational numbers unaccounted for and therefore uncountable using today's math. But I still think we're being a little too proud of our accomplishments to date in mathematics when we state that we know that there will never be a way to list all irrational numbers.

Fraggle Rocker

05-25-06, 12:22 PM

Absane

05-25-06, 12:31 PM

Well, there are formulas for any number you want... e-1 = 1 - 1/1! + 1/2! - 1/3! +..., for example. Euler's constant is lim(x->oo) (1 + 1/2 + 1/3 + 1/4 + ... x) - ln(x).

But essentially here is the deal. When you list all the rational numbers, and assume you have listed all of them, you naturally try to create a new one to add to the list. You cannot, as you will always find that one already in the list.

As for irrational number, you do the same thing. You assume you listed them all. Then you try to create a new number that is not in the list, and you do! Therefore, you assumption that you listed them all is false. How can a school count it's students if it does not have all the students present to be counted?

I think your arguement would (given enough time) come down to arguing the axioms of mathematics (as you seem to be suggestion "new math."). I can take that, as they are just assumed anyway. There is no way to prove them, as was proved by Godel's Incompleteness Theorem's.

Absane

05-28-06, 11:00 PM

Is this an ordered list of all numbers, rational and irrational?

The integer part is trivial. The fractional parts, in binary notation:

.1, .01, .11, .001, .101, .011, .111, .0001, .1001, etc.

It's just counting from one to infinity, reversing the order of the bits, and putting a binary point in front of it. The leading zeros become trailing zeros and by the same convention are not written.

There cannot be any number which is not in that series or the integrity of our numbering system is called into question. Its infinitude is exactly the same as that of integers because they map one-to-one.

All numbers can be expressed as (A, B) where both are positive integers. B is the fractional part written backwards and its place in my list is defined by counting.

Are you asking if the set {.1, .01, .11, .001, .101, .011, .111, .0001, .1001, ...} Forms the interval (0,1) ⊂ R?

And also, if that is the case, since we found a way to line up the all the numbers in (0,1), we can expand on that for all R and therefore R is countable. Corollary, irrationals are countable?

I hope I understand this right :)

Fraggle Rocker

05-28-06, 11:28 PM

Are you asking if the set {.1, .01, .11, .001, .101, .011, .111, .0001, .1001, ...} Forms the interval (0,1) . . . R?

And also, if that is the case, since we found a way to line up the all the numbers in (0,1), we can expand on that for all R and therefore R is countable. Corollary, irrationals are countable?

I hope I understand this right :)I don't understand the notation but I agree with the words.

Just as you can line up all the integers, regardless of the number of digits after the leading zeros, this way you can line up all the fractions, regardless of the number of digits before the trailing zeros. Am I correct that all fractions include all irrational numbers? If so, then it appears that you can list all irrational numbers and the list is exactly the same size (in both length and width, as it turns out) as the list of integers.

Pete

05-29-06, 12:07 AM

Is this an ordered list of all numbers, rational and irrational?

The integer part is trivial. The fractional parts, in binary notation:

.1, .01, .11, .001, .101, .011, .111, .0001, .1001, etc.

It's just counting from one to infinity, reversing the order of the bits, and putting a binary point in front of it. The leading zeros become trailing zeros and by the same convention are not written.

There cannot be any number which is not in that series or the integrity of our numbering system is called into question. Its infinitude is exactly the same as that of integers because they map one-to-one.

All numbers can be expressed as (A, B) where both are positive integers. B is the fractional part written backwards and its place in my list is defined by counting.
Hi Fraggle Rocker,
This list contains no irrational numbers, and not all rational numbers (what is the sequence number of 1/3, for example).

Zephyr

05-29-06, 04:54 AM

Absane, you're thinking of Cantor's diagonal argument (http://en.wikipedia.org/wiki/Cantor's_diagonal_argument)? I think it relies on the countably infinite number of digits you can have in a real number in [0, 1). So as far as you count the numbers to try and include a new one, you can count the digits and exclude it again.

Fraggle, you can say that R is bigger than N because it's easy to count N using R but impossible the other way around. And you can prove that finding power sets (http://en.wikipedia.org/wiki/Power_set) gives you even bigger sets. Although mathematicians who constantly talk about the size of their sets may be compensating for something...

Absane

05-29-06, 10:07 AM

Zephyr, yes that is what I am talking about. I am just trying to explain it 20 different ways. I provided a link in one of my posts that explains the diagonal argument. What it really has turned into now is the fact that we can never "line up" the irrationals so they may be counted.

Absane

05-29-06, 10:07 AM

I got a post in the works and I was aabout to send it, but I lost almost all of it so I am having to start from stratch.. and I got work :( On memorial day...

Zephyr

05-29-06, 10:41 AM

I've never seen a proof that did the irrationals directly ... rather by contradiction that if both Q and R\Q were countable, R would be.

Fraggle Rocker

05-29-06, 11:16 AM

This list contains no irrational numbers, and not all rational numbers (what is the sequence number of 1/3, for example).This list contains all numbers if the integrity of our numbering system is taken for granted. Any number can be expressed in binary notation. (I could haved done it in decimal but I assume that we're all scientists here and binary was easier.) I think the problem you're driving at is that some finite numbers have an infinite number of digits. I can describe to you with complete precision how to navigate down my list to the number 1/3, which is .01010101... in binary and therefore has a sequence number of 10101010... And if you take my instructions you will indeed find it. Except of course for the fact that finding it will take an infinite amount of time.

The fact that my way of sorting fractions gives a one-to-one mapping between integers and fractions troubles me. If I can count integers, then why doesn't this automatically imply that I can also count anything they can map to?

I guess it's because an integer with an infinite number of digits has an infinite value, whereas all fractions have finite values. Does it violate the definition of countability to say that you have to count to infinity to count 1/3, much less pi? Or is assigning fractions this kind of countability just another way of saying that the infinity of fractions is of a larger order than the infinity of integers?

Absane

05-29-06, 07:19 PM

Fraggle.. the thing with counting, in the natural sense, is that if I asked you "what was the nth number you counted" you could tell me. Make sense? It should also make sense that if I pointed at something that was counted at some point, you should be able to tell me when you counted it. So if I ask when did you count the square root of 2, when did you count it? 1? 10? 1929? Maybe you say infinity.. but infinity is not a subset of the natural numbers.

I am still working on that damned reply.. I am feeling pretty ill right now because I ate almost nothing all day and consumed too many sugary drinks :(

Absane

05-29-06, 07:35 PM

If you want the definition of countability, here it is:

A nonempty set "A" is said to be countable if and only if there exists a function f: N->A such that it is surjective (onto). N refers to the natural numbers, N = {1, 2, 3, 4, ... }

This means in the direction we are going (If there exists a function f, the A is countable), we have to assign every number in A to at least one natural number and that every natural number must be assigned one value in A.

The definition of countable infinite is this: A is CI if there exists a one-to-one and onto function f: N -> A.

So, for one natural number, there must be one value of A.. and every value of A must have one value in N, all unique.

I mean, you can skip the binary bit and go straight to decimal using the same method...

0.1, 0.2, ..., 0.01, 0.11, ..., 0.02, ... to infinity.
The union of all the values does in fact equal every number in from zero to one (non inclusive) but we still cannot count every number, only terminating rationals.

Pete

05-29-06, 07:37 PM

Hi Fraggle Rocker,
This list contains all numbers if the integrity of our numbering system is taken for granted.
I don't see it. I don't know what you mean by "the integrity of our numbering system", but I do see that the list does not contain all numbers.

Any number can be expressed in binary notation. (I could haved done it in decimal but I assume that we're all scientists here and binary was easier.) I think the problem you're driving at is that some finite numbers have an infinite number of digits.
That's right... If your list is to contain all numbers, then your list must include numbers with infinite digits. Does it?

I can describe to you with complete precision how to navigate down my list to the number 1/3, which is .01010101... in binary and therefore has a sequence number of 10101010... And if you take my instructions you will indeed find it. Except of course for the fact that finding it will take an infinite amount of time.
Hmm... If I will find it, then I must be able to find it in a finite time. If it takes an infinite time, then I will never find it, I think.

The fact that my way of sorting fractions gives a one-to-one mapping between integers and fractions troubles me.
Now we're on to something.
I think that it does not, in fact, give a one-to-one mapping between integers and fractions.
I think that one-to-one mapping means that for each finite integer, you must be able to find a matching finite fraction, and for each finite fraction, you must be able to find a matching finite integer..
If I can count integers, then why doesn't this automatically imply that I can also count anything they can map to?
You're correct. You can count anything that map to the integers.

I guess it's because an integer with an infinite number of digits has an infinite value
This could be a problem - is there such a thing as an infinite integer? I think that integers might be finite by definition.
whereas all fractions have finite values.
But all integers are fractions, therefore if all fractions are finite then all integers are also finite, right?

Does it violate the definition of countability to say that you have to count to infinity to count 1/3, much less pi?
I think it violates the definition of one-to-one mapping.

Pete

05-29-06, 07:40 PM

Word of the day - surjective.

Thanks Absane!

Absane

05-29-06, 08:06 PM

but I do see that the list does not contain all numbers.

Well, as I said in my previous post, his list DOES include every number from zero to one, non-inclusive.

That's right... If your list is to contain all numbers, then your list must include numbers with infinite digits. Does it?

It does.

Hmm... If I will find it, then I must be able to find it in a finite time. If it takes an infinite time, then I will never find it, I think.

You must be able to find the N that corresponds with it in a finite amount of time, since the value in N is in fact finite.

Now we're on to something.
I think that it does not, in fact, give a one-to-one mapping between integers and fractions.
I think that one-to-one mapping means that for each finite integer, you must be able to find a matching finite fraction, and for each finite fraction, you must be able to find a matching finite integer..

His list is in fact countable, as I stated. It is just not countable in the way he wants or thinks it is.

Pete

05-29-06, 09:00 PM

Well, as I said in my previous post, his list DOES include every number from zero to one, non-inclusive.
Can you prove it?

That's right... If your list is to contain all numbers, then your list must include numbers with infinite digits. Does it?
It does
I'll have to defer to you authority on this one, since you obviously have more mathematical education than I. But I'm not comfortable with it!

You must be able to find the N that corresponds with it in a finite amount of time, since the value in N is in fact finite.
Then what is its value? What finite value in N corresponds with 1/3 in Fraggle's list?

His list is in fact countable, as I stated. It is just not countable in the way he wants or thinks it is.
His list is certainly countable, but I think that there is no surjective function that maps the items in his list onto the rationals, therefore I think that the list is irrelevant to the question of whether the rationals are countable.

Fraggle Rocker

05-29-06, 09:28 PM

I do see that the list does not contain all numbers..1 - that's all one-bit numbers.
.01, .11 - that's all two-bit numbers.
.001, .101, .011, .111 - that's all three-bit numbers.
.0001, .1001, .0101, .1101, .0011, .1011, .0111, .1111 - that's all four-bit numbers.
Etc.

It's just counting from one to infinity and reversing the order of the bits. It contains all numbers (between zero and one), it is mappable to integers (with the pesky problem of finite fractions mapping to integers of finite length), and it's ordered in the same sequence as the mapped integers.If your list is to contain all numbers, then your list must include numbers with infinite digits. Does it?Yes. They're all at the bottom of the list. But you can't actually see them because the list is infinitely long. Then again I suppose you couldn't "see" one of them anyway because you could only see the portion of it transcribed in a string of digits of arbitrary finite length.I think that it does not, in fact, give a one-to-one mapping between integers and fractions. I think that one-to-one mapping means that for each finite integer, you must be able to find a matching finite fraction, and for each finite fraction, you must be able to find a matching finite integer.Yes, I understand that now.This could be a problem - is there such a thing as an infinite integer? I think that integers might be finite by definition.I'm not sure what the definition of an integer is. I'm still struggling through the Wikipedia definition of "surjective." :) But I thought the definition hinged on not having a fractional part. A "cardinal number" as we say in linguistics. I just don't know how to say that in proper mathematical terms.But all integers are fractions, therefore if all fractions are finite then all integers are also finite, right?No, for the purpose of this discussion an integer has the the part to the right of the decimal (or binary) point equal zero and a fraction has the part to the left equal zero. Using standard definitions, though, an integer is indeed a fraction with the denominator equal one.

To sum up, I see the error of my ways. I stick by my guns and maintain that my series is an ordered list of all possible fractions if it is allowed to go to infinity. But I agree that it does not satisfy the proper definition of "countable."

The definition of "surjective" is still in question. :)

Absane

05-29-06, 09:42 PM

Surjective means this:

Well, a function is a mapping of set A to set B, such that every element in A has a value in B and that each value in A cannot have more than one value in B.

When the function is said to be surjective, every element in B must have a value in A, but it does not have to be unique.

For example, Let A = {1, 2, 3} and B = {4, 5, 6}

A function f:A->B might take the values (1,4) (2, 6) (3, 6). This is a function, as every value in A is defined in B and each value is unique to that in A. However, it is not surjective because 5 is not defined in f as a value for an element in A.

An example of a surjective function g:A->B could be (1,4) (2,6) (3,5).

Understand? maybe now you can reply to my post :) I hope!

It's fairly interesting to note that if the cardinality (that is, the "size") of the codomain (B in the case) is greater than the cardinality of the domain (A in this case), then an onto function cannot exist. So if A = N (all the natural numbers) and we cannot create an onto function to all R (or (0,1) in your case) then it seems the codomain's cardinality is in fact "bigger" than the domain. cadrinality of N = infinity and cadrinality of R is infinity.. seems R is bigger :) One infinity greater than the other. However, this is nothing new. Cantor showed this many many years ago.

I have a lot of fun telling people this when I am drunk... they think I am not serious. hehe.

dauthus

06-15-06, 12:44 AM

you may also want to refer to this system

number of zeros
(10 to the power of)

3 thousand
6 million
9 billion
12 trillion
15 quadrillion
18 quintillion
21 sextillion
24 septillion
27 octillion
30 nonillion
33 decillion
36 undecillion
39 duodecillion
42 tredecillion
45 quattuordecillion
48 quindecillion
51 sexdecillion
54 septdecillion
57 octodecillion
60 novemdecillion
100 googol
googol googolplex

Fraggle Rocker

06-15-06, 08:33 AM

you may also want to refer to this system. . . 12 trillion. . . 21 sextillion. . . 54 septdecillionBearing in mind that it is not universal, as has been mentioned in the earlier postings on this thread over the years. Much of the world refers to this as the American system, although it arguably originated in France. Many other countries use a power-of-six paradigm. Million=6, billion=12, trillion=18, etc. It's a little more intuitive because "all" you have to do is translate the Latin prefix into your national language and multiply by six to get the number of zeros, instead of performing the extra step of adding one before multiplying by three. But of course it's more cumbersome because 10^22, for example, must be pronounced "ten thousand trillion." Which is a real mouthful for languages whose grammar requires this to be rendered as "ten thousands of trillions of..." (Some countries call this a "trilliard," which probably makes them wonder what we're doing in all of our gaudily advertised "billiard parlors.")

Also bearing in mind that this is still a bit of an elite exercise. There appears to be no formal consensus on the precise form of some of those higher prefixes. You're more likely to run into "septemdecillion," which is proper Latin, than "septdecillion." And "sexillion" vies with "sextillion" since we can't seem to make up our minds whether we're drawing from the Latin cardinal or ordinal numeral series.

Gadren

06-16-06, 08:31 PM

:eek: Wow! I had never known it was all this confusing... I guess this is why it's better to use scientific notation. ;)

Absane

06-16-06, 09:26 PM

:eek: Wow! I had never known it was all this confusing... I guess this is why it's better to use scientific notation. ;)

Until you got 3 significant digits and you need something bigger than trillion ;)

Mickmeister

02-05-07, 11:14 PM

Thats why when I saw $50 Billion worth of bonds it wasn't worth any more than £35 Thousand Million's (which is are also called Billion's)

I always thought that it was much more logical say thousand million instead of billion. It is more easily distinguishable in vocal communications. I have seen many times where people mistaken billion for million, whereas they would not if it was thousand-million.

Fraggle Rocker

02-05-07, 11:49 PM

I always thought that it was much more logical to say thousand million instead of billion. It is more easily distinguishable in vocal communications. I have seen many times where people mistaken billion for million, whereas they would not if it was thousand-million.It's logical if you only have one or two significant digits. If someone said to me, "The GDP of Earth is nineteen thousand seven hundred eighty-eight billion six hundred seventy-two thousand four hundred thirteen million nine hundred eight thousand five hundred twenty dollars," I would not be able to parse it.

Nineteen quadrillion seven hundred eighty-eight trillion six hundred seventy two billion four hundred thirteen million nine hundred eight thousand five hundred twenty dollars is easier.

Pete

02-05-07, 11:54 PM

Eight bumps...

Nickelodeon

02-14-07, 09:46 AM

Nineteen quadrillion seven hundred eighty-eight trillion six hundred seventy two billion four hundred thirteen million nine hundred eight thousand five hundred twenty dollars is easier.
Is that the US debt now?

Mickmeister

05-07-08, 09:59 PM

million = 106
billion = 109
trillion = 1012
quadrillion = 1015
quintillion = 1018
hexillion = 1021
heptillion = 1024
octillion = 1027
nonillion = 1030
decillion = 1033
unodecillion = 1036
duodecillion = 1039
etc.

hexillion and heptillion are incorrect. It's sextillion and septillion

Pete

05-07-08, 10:30 PM

You dredged up a 15-month old thread for that?

Fraggle Rocker

05-07-08, 11:43 PM

You dredged up a 15-month old thread for that?Particulary since post #128 shows the correct names.

Mick, if you're going to commit thread necromancy at least do it right and read it before you post. Don't Google one post and respond to it without checking the rest of the thread. Chances are, somebody already said what you're about to say and that's why the discussion went dormant.

-- Note from a Moderator (although not the moderator of this subforum).

The Janitor

06-03-08, 12:41 AM

quantum_wave

02-09-09, 08:34 AM

I want my own big number. It isn't really very big vs. the really big numbers mentioned in this thread, but still it is pretty big and the name hasn't been used because I searched Google and SciForums and it is not there, and it doesn't show up in the ieSpell dictionary.

I'm going to call it a bezillion. A bezillion is a googol divided by 10. A googol is a 1 followed by 100 zeros, and a bezillion is a 1 followed by 99 zeros.

You may use it when the occasion comes up :).

I'll check Google later and see if I have establised a bezillion on the web.

John Connellan

02-09-09, 12:26 PM

I think that there should be a limit to numbers. I think the number of Planck volumes in the universe should be the upper limit for numbers (which I think is 1.92 x 10^184 for the observable universe).

This would mean there should be no numbers an order of magnitude bigger than googol (e.g. googolplex) as there is no need for them. Numbers like this will never count anything.

I know we do not yet know the number of Planck volumes in the whole universe but whatever number it is should be the limit.

quantum_wave

02-09-09, 12:41 PM

madanthonywayne

02-09-09, 05:39 PM

What comes after trillion? Then after that...?
Theyre going to coin a new term for what comes after a trillion, it's an Obama. It's what we'll have to use to measure the US national debt if his "stimulus" package passes.

quantum_wave

02-09-09, 05:45 PM

How about calling it an obillian?

Pete

02-09-09, 06:18 PM

:yay: 10! 10 bumps! Hooray! :yay:

Since this thread was started seven years ago, it has gone dormant and been reawakened on ten separate occasions.

I think that's cause for celebration! :xctd:

quantum_wave

02-09-09, 06:26 PM

Some threads are just too good to let die :D.

Fraggle Rocker

02-09-09, 08:18 PM

I'm going to call it a bezillion.You heard about the time that Cheney walked into the Oval Office and said, "Mr. President, yesterday was a terrible day in Iraq. Three Brazilian soliders were killed." Bush's face turned ashen and he crumpled in his chair. Everyone was really impressed that he took it so hard, and they all politely left except Cheney. When they were gone he raised his teary head and said, "Dick, you know that I was never all that good in math, or in any other subject for that matter. Just exactly how much is a brazillion?" A bezillion is a googol divided by 10. A googol is a 1 followed by 100 zeros, and a bezillion is a 1 followed by 99 zeros.Since the number of zeroes is divisible by three, there's already a handy name for that number. It's a duotrigintillion, three times (32+1) zeroes. (Check my Latin, anybody!)I think that there should be a limit to numbers. I think the number of Planck volumes in the universe should be the upper limit for numbers (which I think is 1.92 x 10^184 for the observable universe).But we use numbers for more than counting. We use them for probability. How many possible ways could all the elementary particles in the universe be arranged?What comes after trillion? Then after that...?That must be a quote of an ancient post. But in case there's anyone reading this thread who doesn't know, check the Wikipedia article on orders of magnitude. (http://en.wikipedia.org/wiki/Orders_of_magnitude_(numbers))

After trillion comes quadrillion, quintillion, sextillion, etc. They use the Latin words for the ordinal numbers.

thinking

02-09-09, 08:23 PM

I don't know about that. Since I consider one of the possibilities to be that the universe is infinite, then we could still find ourselves dealing with numbers much bigger than a googolplex. Maybe our "observable universe" and the unobservable portion that you would add to account for the difference between the observed universe and the whole finite thing are just a tiny arena of a potentially infinite greater universe :shrug:.

the Universe is infinite , but so is energy/matter , as far as existence goes

but also the Universe has limits

for instance on limits;

I give you a task , I ask you to knock down the CN Tower, starting at its base , with a hockey stick , can you do it ?

once the stick it is broken no repairs are allowed

therefore the task is impossible and therefore it shows the Universe has limits

quantum_wave

02-09-09, 08:44 PM

You heard about the time that Cheney walked into the Oval Office and said, "Mr. President, yesterday was a terrible day in Iraq. Three Brazilian soliders were killed." Bush's face turned ashen and he crumpled in his chair. Everyone was really impressed that he took it so hard, and they all politely left except Cheney. When they were gone he raised his teary head and said, "Dick, you know that I was never all that good in math, or in any other subject for that matter. Just exactly how much is a brazillion?"I had to laugh pretty hard at that :roflmao:
Since the number of zeroes is divisible by three, there's already a handy name for that number. It's a duotrigintillion, three times (32+1) zeroes. (Check my Latin, anybody!).I respect your grasp of the language and the numbers, and I don't doubt you about the duotrigintillion. However, as you are also certainly aware, some numbers that have zeros that are divisible by three go by more than one name. Billion in America is a trillion in Europe I believe. I don't remember the European name for what America calls a billion, but there is a different name for it.

Therefore it shouldn't be considered unprecedented to have two names for the 99 zero number, right; duotrigintillion and bezillion.

quantum_wave

02-09-09, 08:46 PM

the Universe is infinite , but so is energy/matter , as far as existence goes

but also the Universe has limits

for instance on limits;

I give you a task , I ask you to knock down the CN Tower, starting at its base , with a hockey stick , can you do it ?

once the stick it is broken no repairs are allowed

therefore the task is impossible and therefore it shows the Universe has limitsAgreed, there are limits. But I bet you can't say that a bezillion times :).

thinking

02-09-09, 09:13 PM

Agreed, there are limits. But I bet you can't say that a bezillion times :).

no need to

limits remember !!

Fraggle Rocker

02-09-09, 10:49 PM

However, as you are also certainly aware, some numbers that have zeros that are divisible by three go by more than one name. Billion in America is a trillion in Europe I believe.It's the other way around. What we call a trillion they call a billion. They group the zeroes by sixes instead of threes and they start right off with "million" being 10*6, a somewhat more elegant system. 10*6=million, 10*12=billion, 10*18=trillion, 10*24=quadrillion, etc. For them, 10*15=one thousand billion.I don't remember the European name for what America calls a billion, but there is a different name for it.They just call it one thousand million. However, since wealth of one billion dollars (by the American paradigm) has become attainable, and there are now dozens of billionaires living (by American terminology), the rest of the world is slowly adapting to our terminology just to avoid confusion. Not to mention the awkwardness of saying "thousand-millionaire.":)Therefore it shouldn't be considered unprecedented to have two names for the 99 zero number, right; duotrigintillion and bezillion.Indeed, but the names are much more prosaic. One duotrigintillion (American terminology) would by one thousand sexadecillion in European terminology. (Again, everyone please feel free to check my Latin, it's not one of my strongest languages.)

BTW: The French use our terminology too.

BTW2: The Germans don't say ein tausend millionen, they call it ein milliard. Check out the German postage stamps during the Great Depression.

John99

02-09-09, 11:03 PM

at the endo th e day it is all just patterns and repetition.

quantum_wave

02-10-09, 06:44 AM

It's the other way around. What we call a trillion they call a billion. They group the zeroes by sixes instead of threes and they start right off with "million" being 10*6, a somewhat more elegant system. 10*6=million, 10*12=billion, 10*18=trillion, 10*24=quadrillion, etc. For them, 10*15=one thousand billion.They just call it one thousand million. However, since wealth of one billion dollars (by the American paradigm) has become attainable, and there are now dozens of billionaires living (by American terminology), the rest of the world is slowly adapting to our terminology just to avoid confusion. Not to mention the awkwardness of saying "thousand-millionaire.":)Indeed, but the names are much more prosaic. One duotrigintillion (American terminology) would by one thousand sexadecillion in European terminology. (Again, everyone please feel free to check my Latin, it's not one of my strongest languages.)

BTW: The French use our terminology too.

BTW2: The Germans don't say ein tausend millionen, they call it ein milliard. Check out the German postage stamps during the Great Depression.It is interesting how much there is to discover about numbers and different cultures. How many zeros does one thousand sexadecillion have and is the American counterpart the same or are we still off by a thousand?

BTW1:This is what Google now has not far from the top when you google "bezillion": A bezillion is a googol divided by 10. A googol is a 1 followed by 100 zeros, and a bezillion is a 1 followed by 99 zeros. ... and the link is to this thread and my post naming the "bezillion". It is history now :).

A bezillion is a googol divided by 10. A googol is a 1 followed by 100 zeros, and a bezillion is a 1 followed by 99 zeros. ... Now a bezillion becomes finite instead of just some exaggerated vague expression like that pesky bazillion or even gazillion.

John Connellan

02-10-09, 11:56 AM

But we use numbers for more than counting. We use them for probability. How many possible ways could all the elementary particles in the universe be arranged?

Very true Fraggle!

Fraggle Rocker

02-19-09, 10:59 AM

How many zeros does one thousand sexadecillion have. . . .?Well it was I who rendered it that way and my intention was to come out with 99 zeroes. If it's wrong, it's my own fault. Feel free to do your own derivation.. . . . and is the American counterpart the same or are we still off by a thousand?Again, my intention was to have everything come out the same. Everyone is invited to peer-review my work, this is after all a place of science.BTW1:This is what Google now has not far from the top when you google "bezillion": A bezillion is a googol divided by 10. A googol is a 1 followed by 100 zeros, and a bezillion is a 1 followed by 99 zeros. ... and the link is to this thread and my post naming the "bezillion". It is history now.SciForums is an academy of only tertiary and quaternary research--and that only on a good day.:) After all, much of what is posted as supporting evidence for hypotheses expressed here is taken from Wikipedia, a source that is specifically excluded as valid reference material by the entire U.S. educational system. I've written Wikipedia articles and I've corrected sometimes-glaring errors in dozens of them.

So... Google --> SciForums --> Wikipedia --> Contributions of dubious validity, eventually edited into some semblance of scholarship --> by contributors like yours truly. How many degrees of separation does that make between a Google hit and "history"?:)A bezillion is a googol divided by 10. A googol is a 1 followed by 100 zeros, and a bezillion is a 1 followed by 99 zeros. ... Now a bezillion becomes finite instead of just some exaggerated vague expression like that pesky bazillion or even gazillion.I liked it better when it was vague. Many cultures find a need for quasi-numbers and their languages have analogs to our "umpteen" and "eleventy."

I especially liked Scrooge McDuck with his "three cubic acres of money." Since an acre is a two-dimensional unit of measurement, there's no such thing as a cubic acre.

The metric prefixes for powers of ten are getting pretty silly: exa-, yatta-, zetta. What are they gonna come up with next, now that they've gotten to Z?

quantum_wave

02-19-09, 11:20 AM

...
I liked it better when it was vague. Many cultures find a need for quasi-numbers and their languages have analogs to our "umpteen" and "eleventy."

I especially liked Scrooge McDuck with his "three cubic acres of money." Since an acre is a two-dimensional unit of measurement, there's no such thing as a cubic acre.

...But you have the highest of standards and the greatest depth of knowledge and research acumen when it comes to these type of things. To me, defining a bezillion as having 99 zeros gives me one little patch of territory, one little contribution to bringing order to the universe.

And defining "bezillion" isn't taking anything away from the cultural need for quasi-numbers since it had no standing as a quasi-number before I defined it. It is not even in my on-line dictionary. Oh sure, there was bazillion and gazillion, but no "bezillion". My work is additive and takes nothing away from the language IMHO.

Of course "bezillion" will never be able to compete with McDuck and his "three cubic ares of money", but I am a mere mortal.

Fraggle Rocker

02-22-09, 08:11 PM

Oh sure, there was bazillion and gazillion, but no "bezillion".The first syllable is unstressed so the vowel becomes a schwa. Bazillion and bezillion are pronounced identically.

quantum_wave

02-23-09, 06:34 PM

Hmm, yes, I guess you are right. At first I found that distressing since I was counting on naming my own number. Granted it is a second name and no where near as official as duotrigintillion which you mentioned earlier. But after some thought I can see where bezillion and bazillion being pronounced the same may have some merit. A person could casually mention the number "bezillion" around the water cooler or at a cocktail party, and then point out the difference between the two as a point of interest. Any argument could be resolved by a quick "google" of bezillion to show that it was named by yours truly to be a googol divided by 10.

Maybe some day it will be used in a scrabble dictionary. That is when I will know that a bezillion has arrived.

Fraggle Rocker

02-23-09, 10:32 PM

Maybe some day it will be used in a Scrabble dictionary. That is when I will know that a bezillion has arrived.The Official Scrabble Players Dictionary or OSPD includes all the words in the five most respected American English dictionaries, so all you have to do is get your word into one of them.

However, the OSPD is not actually used in any country's Scrabble tournaments. American tournaments use the Official Club and Tournament Word List. I have no idea how it is compiled. Politics and political correctness play a part; there was a big furore over the benighted slang verb "jew" in lower-case, as "to jew down" a price.

quantum_wave

02-24-09, 07:59 AM

...However, the OSPD is not actually used in any country's Scrabble tournaments. American tournaments use the Official Club and Tournament Word List. I have no idea how it is compiled. Politics and political correctness play a part; there was a big furore over the benighted slang verb "jew" in lower-case, as "to jew down" a price.Funny you should mention that. I personally stepped on that land mine in the 1980's while playing Scrabble with my Jewish friend. But for all I know he was just pretending to be offended to keep me from getting the points.

StrangerInAStrangeLa

02-26-09, 01:43 AM

You're thinking of "googol": 10100
googolplex: 10googol

At billion, it starts up a prefix thing.
1,000,000,000-billion
1,000,000,000,000-trillion
1,000,000,000,000,000-quadrillion
1,000,000,000,000,000,000-quintillion

and it goes from there most of the way.

a google, 1 times 10 to the 100th, was named by a mathmatician's three(or somewhere around there)-year-old, when asked about "what to call a 1 with 100 zeroes behind it.

Don't neglect the googleplex which is a (google)**google a number so large that it cannot be written down.

1 person spells googol correctly. A few posts later 2 people misspell it as google.

Is this a joke???

Pete

02-26-09, 03:11 AM

Yes, a 6.5 year old joke.

Fraggle Rocker

02-26-09, 11:04 AM

Not to mention he got it wrong: A googolplex = 10^googol, not googol^googol.

I remember on "The Simpsons," their town had a multiplex movie theater so big that it was called the Googolplex.

John99

03-01-09, 05:21 AM

million, billion, trillion... then what?

you can call it whatever you want...and it wont make any difference. NONE.

Fraggle Rocker

03-01-09, 03:55 PM

you can call it whatever you want...and it wont make any difference. NONE.Some people become influential, and words they use catch on. Perhaps QW will be one of them. Cleveland disc jockey Alan Freed is credited with naming "rock and roll" music.

StrangerInAStrangeLa

03-01-09, 11:43 PM

Perhaps the word camplex will catch on.

colin

03-25-09, 04:42 PM

Well thx for helping me out guys, the reason i came here was because I was looking something up on supernovas and it said that the power of a supernova is
one-million tons of TNT. So out of curiosity I figured out how much fire-power that would be and it was:1,000,000,000,000,000,000,000,000,000, and i thought to myself WTF? How do i pronounce that...? So i looked it up and found that it was one-hundred septillion in the U.S. Ty, Ty.

Fraggle Rocker

03-28-09, 04:22 PM

. . . . the power of a supernova is one-million tons of TNT.That can't be right. We've built nuclear bombs that produce the energy of fifty million tons (they're called "megatons") of TNT.. . . . I figured out how much fire-power that would be and it was:1,000,000,000,000,000,000,000,000,000. . . .I don't understand. You seem to have some mistakes or omissions in your transcription. How does that number represent one million tons?So i looked it up and found that it was one-hundred septillion in the U.S.Another transcription error. The number you wrote is one octillion in the U.S and France. One hundred septillion would have one less zero.

Oli

03-28-09, 10:19 PM

So out of curiosity I figured out how much fire-power that would be and it was:1,000,000,000,000,000,000,000,000,000
And the units of "fire power" would be....? :rolleyes:

Xylene

03-28-09, 10:23 PM

As I've always understood it, 1,000,000 = 1 million
1,000,000,000 = 1 thousand million (in the old British system of counting)
1,000,000,000,000 = 1 billion (1 million multiplied by itself, hence 10^12)
therefore, using that system 1 million^3 = 1 trillion (10^18)
1 quadillion = 1 million^4 (10^24)
1 quintillion = 1 million^5 (10^30)
1 sextillion = 1 million ^6 (10^ 36)
1 septillion = 1 million^7 (10^42)
1 octillion = 1 million^8 (10^48)
1 nontillion = 1 million^9 (10^54)
1 dectillion = 1 million^10 (10^60) (or decatillion)

Fraggle Rocker

03-28-09, 10:37 PM

1 quadillion = 1 million^4 (10^24); 1 nontillion = 1 million^9 (10^54); 1 dectillion = 1 million^10 (10^60) (or decatillion)You've got the British/German paradigm right but some of the words are slightly off. It's quadrillion, nonillion and decillion. From "trillion" forward, the morphemes are taken from the Latin series of ordinal numbers.

I've been told that the British are grudgingly adopting our definition of "billion." There are now so many people with wealth in excess of $1,000,000,000 that we need a name for them, and "thousand-millionaire" just isn't euphonious--and it doesn't fit very well into a headline either. So they've started using the American word "billionaire."

eburacum45

03-30-09, 04:39 AM

I've been told that the British are grudgingly adopting our definition of "billion."We've been using Billion= 10e9 since the '80s at least. Old billions are rarely used these days.

Fraggle Rocker

03-30-09, 10:52 AM

We've been using Billion= 10e9 since the '80s at least. Old billions are rarely used these days.Yeah, that's about when billionaires became plentiful enough to be spoken about generically. Today there are almost four hundred in the USA and more than two hundred in the rest of the world. (Net worth measured in US dollars.)

Do you still call 10^18 a trillion? If so, what are 10^12 and 10^15?

quadraphonics

03-30-09, 05:01 PM

We've been using Billion= 10e9 since the '80s at least. Old billions are rarely used these days.

Yeah, I get the impression that the only place people actually use the "milliard" and "thousand million" and so on is in internet threads like this one.

scott1987

09-23-09, 11:23 PM

Fraggle Rocker

09-24-09, 11:48 AM

I don't see how atoms has anything to do with how high a number can goEven if it did, it's easy to transcend that limit. Count the number of possible paths through the universe if you visit every atom once.

Then save your descriptions of each path in a catalog and count the number of ways you could sort the catalog. That becomes the data that comprises a new catalog, which you can sort...

quantum_wave

09-24-09, 12:25 PM

Wow I just wanted to know what came after a trillion but I learned alot more than that from this thread but I dont think there is a finate number just throw a zero at the end and you can keep going for eternity. I dont see how atoms has anything to do with how high a number can goHi scott1987. I was trying to find the post that you mention showing how atoms have something to do with how high a number can go. Was it on this thread? Link?

Even if it did, it's easy to transcend that limit. Count the number of possible paths through the universe if you visit every atom once.

Then save your descriptions of each path in a catalog and count the number of ways you could sort the catalog. That becomes the data that comprises a new catalog, which you can sort...True, we would be able to get some pretty high numbers using just that one method. But still I think that the number would be finite if the number of atoms in the universe at any point in time is finite (I find that debatable) and if you could keep all of the original atoms in the set while you wile away your time constructing and sorting.

Even adding zeros would always result in a finite number ... unless like scott1987 suggests, you could keep adding zeros for eternity. Since eternity is itself an infinite, then the limit that you approach as you move toward eternity by adding zeros is an infinite number. But you never get to eternity and so you never reach the infinite limit and would therefore always have an finite number at any point prior to eternity. I think that is an example of the reason that "infinite" is a concept and never a reality. What says you FR?

X-Man2

09-24-09, 04:21 PM

Here's a site that shows you numbers in pennies. Each link 1-18 shows you what a certain amount of pennies looks like, increasing in numbers as you go up. And also has links to some other sites.

http://www.kokogiak.com/megapenny/nineteen.asp

So any Smart and clever people here that can tell us how many pennies would it take to cover the entire earth,i penny high? Me don't :shrug:

Fraggle Rocker

09-24-09, 06:15 PM

I was trying to find the post that you mention showing how atoms have something to do with how high a number can go.It's not that the number of atoms in the universe sets a natural limit on the size of numbers. Numbers, like all mathematics, are abstractions after all. That's why mathematical theories can be proven absolutely true, whereas scientific theories can only be proven true beyond a reasonable doubt and are in fact occasionally falsified. Mathematical theories are derived from abstractions, rather than from empirical observations of the natural universe.

I'm not going to look this up--I'll leave that for one of you young'uns with nothing to do but play videogames--but as I recall it was absurdly easy to write a number that is greater than the number of atoms in the universe. It may have been a googolplex, 10^[10^(10^2)], one with a googol zeros.True, we would be able to get some pretty high numbers using just that one method. But still I think that the number would be finite. . . .Well of course: all numbers are finite. The eight on its side representing infinity is not a number, it's a mathematical symbol. Some mathematical symbols like pi and e are numbers, to be sure, but not all of them.. . . .if the number of atoms in the universe at any point in time is finite (I find that debatable). . . .Why? I have never encountered a model of the natural universe which contains an infinite number of atoms. Have you?Since eternity is itself an infinite, then the limit that you approach as you move toward eternity by adding zeros is an infinite number.Then it's not really a limit, is it? Don't try to get away with that statement on my board (Linguistics).;)I think that is an example of the reason that "infinite" is a concept and never a reality.As I said, mathematics deals with abstractions--concepts. Those abstractions or concepts map very well to the natural universe, which is why mathematics is so useful. One cow plus one cow always equals two cows. But not all of those abstractions map so closely to physical objects. Infinity is one that does not. That doesn't make it any less useful, especially to scientists.

quantum_wave

09-26-09, 07:29 AM

...
Why? I have never encountered a model of the natural universe which contains an infinite number of atoms. Have you?

Then it's not really a limit, is it? Don't try to get away with that statement on my board (Linguistics).;)Sorry, I would never ...

As I said, mathematics deals with abstractions--concepts. Those abstractions or concepts map very well to the natural universe, which is why mathematics is so useful. One cow plus one cow always equals two cows. But not all of those abstractions map so closely to physical objects. Infinity is one that does not. That doesn't make it any less useful, especially to scientists.Agreed. Infinity, the concept, is useful. And the natural universe could have always existed and could be infinite. If that were the case then it could contain an infinite number of atoms, IMHO.

Fraggle Rocker

09-27-09, 12:55 PM

And the natural universe could have always existed and could be infinite. If that were the case then it could contain an infinite number of atoms, IMHO.Regardless of how long the universe has existed, our observations consistently indicate that the dimensions of the portion of it that contains matter are finite.

As I have noted before, if you graph time on a log scale, that puts the Big Bang at minus infinity. There's no good reason that time can't have an Absolute Zero, like temperature.

quantum_wave

09-27-09, 01:36 PM

Regardless of how long the universe has existed, our observations consistently indicate that the dimensions of the portion of it that contains matter are finite.

I would agree if you had said that the portion of it that we can observe contains a finite amount of matter.
As I have noted before, if you graph time on a log scale, that puts the Big Bang at minus infinity. There's no good reason that time can't have an Absolute Zero, like temperature.If I interpret that it sounds like you are saying that according to Big Bang Theory there was a beginning of time, and then I would agree.

I'm one of those lost souls who considers the possibilities and there are alternatives to BBT that could explain what we observe with fewer unintuitive hurdles. One alternative as I mentioned is that the universe has always existed, the Big Bang was not a single event but a characteristic of the landscape of the greater universe where big bangs could be common evernts, and that greater universe could contain an infinite amount of matter and energy. Thus there could be an infinite number of atoms in the greater universe.

But I'm not a professional so I am free to think what I want :).

Fraggle Rocker

09-28-09, 11:23 AM

I would agree if you had said that the portion of it that we can observe contains a finite amount of matter.As I understand it, the limits of our ability to observe extend well beyond the outer boundary of the collection of matter that we refer to as "the universe," and there's literally nothing there. Of course there is energy there, since light from all of the sources in "the universe" is traveling in all directions and some of it is headed outward.If I interpret that it sounds like you are saying that according to Big Bang Theory there was a beginning of time, and then I would agree.That is what I'm hypothesizing.I'm one of those lost souls who considers the possibilities and there are alternatives to BBT that could explain what we observe with fewer unintuitive hurdles.The universe is indifferent to the limitations of our intuition. If it could speak it would be saying something like, "Get over it."One alternative as I mentioned is that the universe has always existed, the Big Bang was not a single event but a characteristic of the landscape of the greater universe where big bangs could be common evernts, and that greater universe could contain an infinite amount of matter and energy. Thus there could be an infinite number of atoms in the greater universe.I have said much the same thing. The biggest problem with the Big Bang model is that it hypothesizes an enormous local reversal of entropy: The sudden existence of organization where there was none.

However, the probability of reversal of entropy is NOT zero. Such an event is, merely, the result of a set of coincidences whose probability is so small as to be safely ignored in scientific work.

If spacetime is infinite, then any possible coincidence can occur. In fact it could occur more than once. Another Big Bang could have occurred a googol light-years from here, or a googol years in the past or future, in which case we'll probably never be able to observe the results.

I'm not a good enough mathematician to assess the probability of this set of coincidences occuring an infinite number of times. If that could actually happen, then the total mass of matter in the REAL universe (as opposed to the tiny portion we know about which includes a lot of empty space between our "little universe" and the next "little universe") might indeed be infinite.But I'm not a professional so I am free to think what I want.We're all here to learn. You don't have to be a "professional" career scientist. All you have to do is respect the scientific method. If your hypothesis is based on logic, is consistent with empirical observations of the natural universe, and does not contradict more than one canonical scientific theory, then we're obliged to treat it with respect until someone falsifies it.

quantum_wave

09-28-09, 12:39 PM

As I understand it, the limits of our ability to observe extend well beyond the outer boundary of the collection of matter that we refer to as "the universe," and there's literally nothing there. Of course there is energy there, since light from all of the sources in "the universe" is traveling in all directions and some of it is headed outward.

That is what I'm hypothesizing.
Check your understanding then. Hubble deep field pics show much younger galaxies in all directions which makes sense because the light that reaches us from them started about 13.7 billion years ago when the expanding arena lit up with young galaxies.

The understanding that you convey about being able to see beyond the youngest galaxies is news to me, especially in BBT. The entire universe is all there is and the space that the BBT universe occupies is all the space there is according to theory. Seeing beyond it isn't an option in BBT, there is no beyond. The radiation is captive of the curvature of spacetime and is contained within the expanding universe as I understand it.

According to BBT the cosmic background radiation is causally connetcted to the big bang and is observed at a near constant 2.7 degrees Kelvin in all dirctions as a remnant of the 100 billion or so degree initial event. But still, the entire CMBR is enclosed in the space that is also causally connected to the Big Bang. In BBT, there is no space, time or energy that did not come into existence at the instant that expansion began. Space inflated in the first 10^30 seconds according the Alan Guth's Inflationary Theory, but still the entire vastness of space began as a very tiny if not infinitely small spacetime that contained every bit of energy that now exists.

There is room for alternatives and discussing them is not against science, just against BBT.

The universe is indifferent to the limitations of our intuition.
Any yet you are saying that BBT is your basis for approaching the discussion from the perspective of there being a beginning of time. If you feel that I am employing intuition and you are applying science as followed by the scientific method then are you aware that Big Bang Theory does not include the Big Bang event itself, it starts with the instant after expansion began.

My intuition as you call it is a disdain for something coming from nothing. Isn't it just as intuitive to say that the entire known universe came from nothing as it is to say that the universe has always existed.

And what I said was that, "I consider the possibilities and there are alternatives to BBT that could explain what we observe with fewer unintuitive hurdles." I'm hopeful that you are not saying that better explanations must be rejected because the universe is indifferent to the limitations of our intuition? After all isn’t it your intuition that there are no possibilities or alternatives that better explain what we observe.

If it could speak it would be saying something like, "Get over it."
I doubt it. If it could speak it would say consider the possibilities and demand reason not intuition on either of our parts.

I have said much the same thing. The biggest problem with the Big Bang model is that it hypothesizes an enormous local reversal of entropy: The sudden existence of organization where there was none.

However, the probability of reversal of entropy is NOT zero. Such an event is, merely, the result of a set of coincidences whose probability is so small as to be safely ignored in scientific work.

I completely agree and though I have heard it mentioned as a possibility of quantum theory and uncertainty, I know of no cosmology based on it.

If spacetime is infinite, then any possible coincidence can occur. In fact it could occur more than once. Another Big Bang could have occurred a googol light-years from here, or a googol years in the past or future, in which case we'll probably never be able to observe the results.
I'm with you on that with stipulations. If that were the case then spacetime would not apply without changes to GR and to the consensus cosmology of BBT.

But to discuss a greater universe where other Big Bangs could have occurred at great distances from us and if expansion continues and accelerates, then the various other possible Big Bang expanding universes would inevitably intersect and overlap at a point in time in the future.

I'm not a good enough mathematician to assess the probability of this set of coincidences occurring an infinite number of times. If that could actually happen, then the total mass of matter in the REAL universe (as opposed to the tiny portion we know about which includes a lot of empty space between our "little universe" and the next "little universe") might indeed be infinite.
I am happy to get that much acknowledgement of such a possibility out of anyone.

We're all here to learn. You don't have to be a "professional" career scientist. All you have to do is respect the scientific method. If your hypothesis is based on logic, is consistent with empirical observations of the natural universe, and does not contradict more than one canonical scientific theory, then we're obliged to treat it with respect until someone falsifies it.
Agreed. And I contend that the alternative that I consider includes a cause for the Big Bang and pre-existing space and energy. Call it intuitive but I call it a logical alternative to the intuition that everything we observe came from nothing without a cause.

We have ventured off topic by talking about a possible universe where the number of atoms is infinite. My point was that if there are an infinite number of atoms then there is no number to represent them, only the symbol eight on its side as you mentioned earlier.

Silvercast

08-28-10, 02:09 AM

A googol is the large number 10^100, that is, the digit 1 followed by one hundred zeros.

I do beleive there is a number larger then googol. But googol CAN infact be written out, case and point.

10,000,000,000,000,000,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000,000,000,000,000

However, googol ALSO (for you super techy nerdy guys who go to school for this) is know by ten duotrigintillion. So assumedly, there is no limit to how big a number can get, because as long as we have those nifty latin prefixes, we can keep going, Oh, btw.

100,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000 One hundred duotrigintillion

Pinwheel

08-28-10, 02:15 AM

I do beleive there is a number larger then googol. But googol CAN infact be written out, case and point.

10,000,000,000,000,000,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000,000,000,000,000.

Is that the size of the next bailout?

Silvercast

08-28-10, 11:27 PM

Is that the size of the next bailout?

More then likely.

Fraggle Rocker

08-29-10, 01:06 AM

I do believe there is a number larger than googol. But googol CAN in fact be written out, case in point.It's called a googolplex, ten to the googolth power or 10^(10^100). A one with a googol zeroes, I promise that you can't write it out. :)

I don't believe the Latin names for powers of a thousand have been defined beyond 10^(3*99) so you wouldn't even be able to write it as a word. (In Europe, powers of a million so they can reach 10^(6*99), which is still woefully inadequate.)

Edit: Oh sorry. Centillion has been coined: 10^(3*100). That means we have uncentillion, 10^(3*101), etc. (And the corresponding series in the European system.) That will get us, with increasing polysyllabic awkwardness, up to 10^(3*999), whose name I will not even try to spell out here. The word milillion 10^(3*1000) is perfectly logical AND conforms to the Latin model, so it is used by some people. (Surely not the nearsighted or the sloppy typists.) However, it has not been officially adopted by the science community. I suppose that would get us to 10^(3*999,999), another name I will not attempt to write out. If anyone decides to coin millionillion 10^(3*1,000,000), please let me know right away. :)

That would, logically, give us googolplexillion 10^(3*(10^100)). Then we could have googolplexillionillion 10*(3*(10^(3*(10^100))). This could go on forever.

Hmmm. In the age of Google (not to be confused with "googol" although they are related), I wonder how long it will be before people start hitting this post and spreading those words throughout cyberspace. Too bad everything on SciForums is public record so we can't copyright this stuff. :(