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3.141592653589793238462643383279502884197169399375 10

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164

http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html

Do you want me to post all 100,000 listed at this site? :eek:

Isn't it interesting that pies are round and the number pi sounds like pie? :m:

No.

I can see you're a real joy to have at parties...

When I was in 7th grade I memorized the first 100 digits because I was bored.

If posting here is the closest you ever get to a party, I feel for you.

This is a Physics & Math forum, remember?

Do you want me to post all 100,000 listed at this site? A recitation of the first 100,001 would be nice.

This is a Physics & Math forum, remember?

Oohhh! Sorry! Sorry for not bein' all professional and everything!

Robot.

SL, I for one thought your statement of pies and round was the most profound account given on this forum.

Thank you *bows regally*

here we have most often square pies, so maybe squaring the pie is in order....ha

Mmmm... Pi...
http://www.samscam.co.uk/images/homereat.gif

A question or puzzle:

If light travels 314159 kms per second in curved space and 299792kms per second in flat space how big is the universe? :)

TRICK QUESTION. The universe doesn't exist because light doesn't travel :m:

WAIT - Are we talking about the real universe or your universe?

TRICK QUESTION. The universe doesn't exist because light doesn't travel :m:

WAIT - Are we talking about the real universe or your universe?

ha......my universe of course....is there any other.....being frame dependant and all....

OK - TRICK QUESTION.

My all CAPS are just fine!

Actually I just remembered the hmmmmm...some of the logic or reasoning to my question. [ only some]

If light travels 314159 kms per second in curved space and 299792kms per second in flat space how big is the universe.

How far does light have to travel in a straight line [ at 299792km per sec]to alllow for a curved- space speed of 314159 kms per sec to scribe a circle.?

say I project a very strong laser straight ahead of me and that laser is never obstructed by anything, how long would it take to hit me in the back of my head? Sort of premise to the question.
Would the answer tell me how big the universe was?

Your question is ill-posed. You are assuming light travels faster in curved space when in fact it does not.

Firstly , apologies to the thread starter as we are obviously off topic.

Your question is ill-posed. You are assuming light travels faster in curved space when in fact it does not.
No I am suggesting that light travels the same speed in curved space as it does in flat space. The relative speed of curved vs flat. for a given "flat " distance.

The hypothesis:
If space is dimensionally curved in all directions then the curved speed would have to be higher along the curve to match the flat speed. [we do know the flat speed already but not the curved speed]
The omni directional curvature of space providing a resistance to lights speed. In other words, the permeability of vacuum [space] for lights travel is determined by this omni curvature.

So if we disassemble the curvature so that it is a single curve the speed of light could be assumed to be 314159 km per sec.

Of course this curved speed of 314159kps is a geometric assumption and is purely speculatve.

thus as the universe expands it would lead to the conclusion that 'c' will decrease. So if the hypothesis was founded we should see an decrease in 'c', which of course we haven't been able to confirm yet.
So the speed of light in "flat" space should be able to tell us the size of the universe.....

Unfortunately I simply can't even imagine the complexity of the math involved.....

edit: prediction change from increase in 'c' to decrease in 'c'

I tend to think of the flat speed of light as being a "spacetime average" or mean speed.

Yuck!

I stopped reading mid-sentence somewhere about:

The relative speed of curved vs flat
there.

Sorry - but I refuse to go down this pot-hole road (I don't want to fall into a pit).

no problem....'tis all abstractions anyway.......

Did anyone read the book "Contact" by Sagan? I love the part where Ellie (after getting back from her trip) starts calculating pi to zillions of decimal places, and then all of a sudden an anomalous string of 1's and 0's occurr, and if you plot them in a square matrix, the image of a circle appears! Supposed to be a message embedded in the very fabric of space by the "engineers" of the universe...

OK - what is the size of the matrix, I'll write a little computer program to reproduce it so we can find our circle ;)

Maybe I'll have better luck writing a program to search for such a pattern - talk about a waste of f'ing time/energy.

OR is that time/space?

Well, the aliens she meets tell her about this. It's one of the mysteries even they (super advanced) haven't been able to figure out...

Nonsense, I don't care how advanced they are. Everything in movies is true - therefore it is imperitive that we find this pattern.

Go for it! (wouldn't that just rock your universe? A pattern embedded in pi...)

I gave it a go and couldn't figure out how to work with hexadecimal numbers (computer language BS - don't go thinking I don't know what a hexadecimal number is!) to use the BBP formula so I gave up :mad:

Oh well. Another universe shattering discovery bites the dust.

Some readers will remember this picture I posted in another pi thread.

As a comparison between a picture generated by random and another generated using Pi.

50000^2
Allocating a grey scale for every pi digit value 0-9
<img src=http://www.paygency.com/Diagrams/both.jpg>

Both look surprisingly like a star scape IMO

I then posted this as joke:
<img src=http://www.paygency.com/Diagrams/pi25000012345.jpg>

Ha! I remember those pictures.

Isn't it interesting that pies are round and the number pi sounds like pie? :m:
In fact, in greek (pi is a greek letter) it sounds like pee, or pea, not like pie

Did anyone read the book "Contact" by Sagan? I love the part where Ellie (after getting back from her trip) starts calculating pi to zillions of decimal places, and then all of a sudden an anomalous string of 1's and 0's occurr, and if you plot them in a square matrix, the image of a circle appears! Supposed to be a message embedded in the very fabric of space by the "engineers" of the universe...

Synchronicity!

I read Contact for the first time only a week ago.

While it' a brilliant idea, it's been annoying me a bit...

I think that Pi isn't part of the "created" Universe - it's a part of fundamental mathematics. I think that mathematical relationships and fundamental constants such as Pi exist necessarily and eternally (to use the language of the theologians), which puts maths on a par with God, existence-wise.

I don't think that even God could put a pattern into Pi.

Synchronicity!

I read Contact for the first time only a week ago.

While it' a brilliant idea, it's been annoying me a bit...

I think that Pi isn't part of the "created" Universe - it's a part of fundamental mathematics. I think that mathematical relationships and fundamental constants such as Pi exist necessarily and eternally (to use the language of the theologians), which puts maths on a par with God, existence-wise.

I don't think that even God could put a pattern into Pi.

But Pete he did and can....[philosophy] with out even taking a theology perspective pi is a pattern for infinite diversity.

I have argued this case before. Pi by nature of it's lack of pattern is in fact a pattern. So often when we look at things we fail to recognise what we are looking at due to the nature of looking from a certain perspective , a position of looking for somethingness if you like. We see no pattern and think hey there is no pattern, but a non-pattern of the Pi variety is in fact a pattern because of it's seemingly absolute non-pattern outcome.

Can't see the forest because we are looking for trees

It could be argued that every space-time co-ordinate or location is unique. Never identicle. Pi is an example of mother natures diversity IMO.

Thus infinite diversity is available to the universe [ End of philosophy]

So pi is more than just a mathematical construct and is an example of how the universe by it's very nature must support this diversity. After all isn't the math of pi just a numerical description [in part] of that universe?

If you wanted to create infinitely diverse universe pi would certainly be a part of your math.

Take this to the religion forum.

Pete: Mathematics is the language of the universe.

Quantum Quack: WTF?

Can we return to the subject of pi please, now who wants apple and who wants cherry? Do you want cream with that

Some readers will remember this picture I posted in another pi thread.

As a comparison between a picture generated by random and another generated using Pi.

50000^2
Allocating a grey scale for every pi digit value 0-9
<img src=http://www.paygency.com/Diagrams/both.jpg>

Both look surprisingly like a star scape IMO

I saw that on TV once, it shows round the clock on the "my cable isn't connected properly" channel

Is anyone surprised by the above?

I'd only be surprised if Pi did not appear random in such a fashion.

Pete: Mathematics is the language of the universe.
It's more than that - Mathematics is the language of all possible Universes.

Well, you can say that... and I cannot argue as I cannot prove that any other possible universe does not exist.

But mathematics is the language of our universe, this much we know to be true. If you want to insist on other possible universes, then you should be the first to accept that patterns can be imbedded into mathematical constants as these constants would change for another "possible" universe.

Whether other Universes actually exist or not is irrelevant.

Mathematics is the languages of all possibilities of existence, regardless of whether such possibilities are actualized - witness our recent discussions of Newtonian universes, and SR-only universes.

I suggest that while physical constants may change, mathematical constants may not.

I suggest that while physical constants may change, mathematical constants may not.
Point accepted. However, I do contend that the alien circle pattern as mentioned by SL is possible given then infinite length on the digits of pi. Some local pattern is bound to happen just by chance. I wouldn't put any meaning into this as the ficticious aliens apparently did, but nevertheless, it would be cool to find.

Pete, I totally agree with you. No matter what universe you inhabit, curvature is curvature. If you set up the mathematical construct called a plane (of zero curvature) and describe a closed curve of uniform constant curvatrue on the plane, and divide the perimeter length of this closed curve by the distance between two points that are diametrically opposed, you will always get the ratio pi.

(that would be a CIRCLE for those of you not living in my universe...)

Is there an algorithm to get any digit of &pi; in binary without knowing any of the preceeding digits - similar to the BBP formula for hexadecimal?

I think the binary immediately follows from the hex...

Every hex digit corresponds to 4 binary digits, so if you know the nth hex digit, you immediately know the 4n-3 to 4n binary digits.

eg if the billionth hex digit is B, then the binary digits from the 3,999,999,997th to 4,000,000,000th are 1011.

Point accepted. However, I do contend that the alien circle pattern as mentioned by SL is possible given then infinite length on the digits of pi. Some local pattern is bound to happen just by chance. I wouldn't put any meaning into this as the ficticious aliens apparently did, but nevertheless, it would be cool to find.
I guess the question is what the chances are of finding said pattern within the first n digits. Or, what is the chance of the first set of 1s and zeros of length greater than 20 being a set of 121 that represent an 11x11 picture of a circle?

Argh, now I have to figure out how this hexadecimal mathematics works in computer language. Damn you.

I guess the question is what the chances are of finding said pattern within the first n digits. Or, what is the chance of the first set of 1s and zeros of length greater than 20 being a set of 121 that represent an 11x11 picture of a circle?
You can find about any code you want in a book of sufficient length. So I imagine you can find any code you want in the digits of pi given a sufficient length of the digits.

Yes, of course... but that's not relevant to what I said.

What is the probability that said pattern (11x11 picture of a circle) could be found in (say) the first 10¹⁰⁰ digits of Pi? Not even worth considering!


What is the probability that the first sequence of 1s and 0s of length 20 or more occurring in Pi would be of length greater than 100? Not even worth considering!

Argh, now I have to figure out how this hexadecimal mathematics works in computer language. Damn you.
:D

What language / environment are you working in?
Often you can represent hex numbers using the 0x prefix: eg 0xC is the same as 12 (but I don't know if that helps!)

Yes, of course... but that's not relevant to what I said.

What is the probability that said pattern (11x11 picture of a circle) could be found in (say) the first 10¹⁰⁰ digits of Pi? Not even worth considering! Any reason why you chose a google digits? I'd say the probability is ~100% ;)


What is the probability that the first sequence of 1s and 0s of length 20 or more occurring in Pi would be of length greater than 100? Not even worth considering! I got lost in the middle of that sentence. Reading from the beginining of the sentence to the end does nothing for me. Let me try end to beginining...


Yeah, that makes no sense. Try it: considering worth even not 100 than greater length of be would pi in occuring more or 20 length of 0s and 1s of sequence first the that probability the is what?

Any reason why you chose a google digits? I'd say the probability is ~100% ;)
And how did you calculate your wild-ass-guess?

I got lost in the middle of that sentence. Reading from the beginining of the sentence to the end does nothing for me. Let me try end to beginining...

I know you can do it!

Imagine that you search the digits of pi from the beginning until you find twenty digits in a row with nothing expect ones and/or zeros.

What is the probability that these twenty digits are the first in a group of 121 that represent a picture of a circle?




Do you get it yet? In the novel, the surprising thing was not that such a sequence could exist in the digits of pi, but that it is was found so early.

This was spelled out pretty explicitly... have you read it?

And how did you calculate your wild-ass-guess? Something about an approximation to a circle using a polygon with google line segments wouldn't fit inside the universe. So someone said once anyway.



I know you can do it!

Imagine that you search the digits of pi from the beginning until you find twenty digits in a row with nothing expect ones and/or zeros.
OK - there in lies the problem. I was considering the binary digits of &pi;, not the decimal digits.



What is the probability that these twenty digits are the first in a group of 121 that represent a picture of a circle? 0.





Do you get it yet? In the novel, the surprising thing was not that such a sequence could exist in the digits of pi, but that it is was found so early.

This was spelled out pretty explicitly... have you read it? No I haven't :D Again, in what base? I'd only consider binary.

I've heard there's a two-line hymn in the language Sanskrit, which gives the value of pi/10 upto a certain number of decmal places, using a system which substitutes the letters of Sanskrit with the 9 digits. That's not very surprising. What is surprising is that apart from the fact that it can be read in two ways, as hymns to two different Hindu Gods, it also contains a formula for extending the value to any number of decimal places. Unfortunately, I don't know Sanskrit, and so cannot verify this. Is there anyone here who does?

I've heard there's a two-line hymn in the language Sanskrit, which gives the value of pi/10 upto a certain number of decmal places, using a system which substitutes the letters of Sanskrit with the 9 digits. That's not very surprising. What is surprising is that apart from the fact that it can be read in two ways, as hymns to two different Hindu Gods, it also contains a formula for extending the value to any number of decimal places. Unfortunately, I don't know Sanskrit, and so cannot verify this. Is there anyone here who does?
And there are vimanas buried with the ancient cities of India as well. I suspect that the meaning of life can be found in Sanskrit too :rolleyes:

And there are vimanas buried with the ancient cities of India as well. I suspect that the meaning of life can be found in Sanskrit too :rolleyes:

Yep. Everything that we have discovered so far, and everything that will ever be discovered, has already been known, hundreds of thousands years ago, and parts have been written down.

This knowledge comes originally from the Atlanteans and Lemurians. Man, because of his arrogance, has created different religions out of their knowledge and formed it egoistically according to race, skincolor, culture and so on.

The Atlanteans weren't like us, they were not egoistic, they loved and knew everything, they could convert energies in every possible way, without any devices. They could also communicate telepathically and lift their vehicles from the ground with their mind's power :)

Old fables tell of them, but people laugh at them :(

Yep. Everything that we have discovered so far, and everything that will ever be discovered, has already been known, hundreds of thousands years ago, and parts have been written down.
:m:

This knowledge comes originally from the Atlanteans and Lemurians. Man, because of his arrogance, has created different religions out of their knowledge and formed it egoistically according to race, skincolor, culture and so on. So was Jesus an Atlantean or Lemurian?

The Atlanteans weren't like us, they were not egoistic, they loved and knew everything, I read Plato, he seemed to believe otherwise. :D

they could convert energies in every possible way, without any devices. They could also communicate telepathically and lift their vehicles from the ground with their mind's power Wait, I've seen this before... Umm - ahh yes, YODA!


Old fables tell of them, but people laugh at them
I always thought George Lucas was a genius. Turns out he was a plagiarist :mad:

Just playing with pi.

I found that if you take every digit 0-9
and divide 360 degrees by that digit every digit ends up in a whole number except 7

360/0 = 360
360/1 = 360
360/2 = 180
360/3 = 120
360/4 = 90
360/5 = 72
360/6 = 60
360/7 = 51.42857143
360/8 = 45
360/9 = 40

Maybe the number 7 in the pi sequence is important....

Yes interesting. I think one reason 360 was chosen (seems arbitrary at first glance) was for just this reason. Makes figuring things in the absence of calculators easier.

Just a minor point: 360/0 = &infin;

Maybe the number 7 in the pi sequence is important....
22/7 is used as an approximation to &pi;.

Yep. Everything that we have discovered so far, and everything that will ever be discovered, has already been known, hundreds of thousands years ago, and parts have been written down.


Please don't push it. How the heck do you support your claim?

360= 2*180= 2^2*90= 2^3*45= 2^4*3*15= 2^4*3^2*5.

The only prime numbers between 1 and 10 are 2, 3, 5, and 7.

Just a minor point: 360/0 = &infin;

360/0 is undefined in the real numbers.

There is (or was?) a group called the Duodecimal society that supported a change to base 12 partly because 12 is 'more divisible' than 10.

QQ:There's nothing special about 7 and pi. 360 is an arbitrary choice for the number of degrees in a circle, you could have just as easily gone with 210 instead, or 2520 if you prefer.

360/0 = ∞

Or more importantly 1/∞ = 0 so 1/0 = ∞, 360 * 1/0 = 360 * ∞ = ∞

That's just how ∞ works.

360 is an arbitrary choice for the number of degrees in a circle
No, 360 was chosen because it has so many factors. It is just easier to work with.

360/0 = ∞

Or more importantly 1/∞ = 0 so 1/0 = ∞, 360 * 1/0 = 360 * ∞ = ∞

That's just how ∞ works.

Infinity is not a real number. Division by 0 is not defined in the real numbers. That's all there is to it.

(yes I do know what a limit is, but those aren't what you've written or how this originally came up in this thread)

No, 360 was chosen because it has so many factors. It is just easier to work with.

You miss the point-there's nothing mathematical compelling us to declare there are 360 degrees in a circle. It's not a 'natural' choice but one of convenience, and my history may be off but I believe it had something to do with a 360 day calender (Babylonians?). A fear of fractions does not constitute a mathematically 'natural' choice, nor does happening to live on a planet that happens to have a 360 day year (or close to it). There is nothing special about 7 and pi based on the fact that 7 does not divide 360 evenly.

Degrees themselves as a unit of measure are not a mathematically natural thing for that matter. You'll notice in most calculus courses, actually all I've ever seen, degrees are quickly dropped for radians as the more natural measure (of course with an explanation of how they relate).

There is (or was?) a group called the Duodecimal society that supported a change to base 12 partly because 12 is 'more divisible' than 10.


That's completely idotic, if you think about it. Because there's always a number which is more divisible than any you give. So maybe you should choose something like 29#. Where p# is similar to the factorial (p!) , but only involving all primes from 2 to p.

Infinity is not a real number. Division by 0 is not defined in the real numbers. That's all there is to it.

Sorry, (or not). Division by zero is quite well defined- as infinity, except in the case where your dividend is also zero. I don't see that this is a difficult concept to grasp. But there <I>are</I> lots of people who shy away when they see some division by zero. I don't understand why they're so afraid.

Infinity is not a real number. Division by 0 is not defined in the real numbers. That's all there is to it. There is no point in blasting nonsense about real numbers. Infinity is the result of dividing by an infinitely small number (i.e. approaching 0). There is nothing too complicated about it.


(yes I do know what a limit is, but those aren't what you've written or how this originally came up in this thread)
It originally came up when QQ said 360/0 = 360 and SL correctly pointed out to him that 360/0 was not 360 and was in fact ∞. What do you not understand? You can not claim division by 0 if you want to only consider a real concievable number - the issue of bringing up "real numbers" is nonsense here.


You miss the point-there's nothing mathematical compelling The point went right over your head. There IS something mathematically compelling to use 360. The many factors of 360 is the mathematically compelling reason. Now if you said there is no physically compelling reason to use 360, then that would be true. 360 degrees in a circle has no physical meaning.

That's completely idotic, if you think about it. Because there's always a number which is more divisible than any you give. So maybe you should choose something like 29#. Where p# is similar to the factorial (p!) , but only involving all primes from 2 to p.

Yep, it's idiotic.


Sorry, (or not). Division by zero is quite well defined as infinity, excpet in the case where you are dividend is also zero. I don't see that this is a difficult concept to grasp. But there are lots of people who shy away when they see some division by zero. I don't understand why they're so afraid.

There's no fear, only your lack of understanding of what the real numbers are and how they are defined. Look up the axioms for a complete ordered field (just the field axioms will suffice), you'll see that division by zero is undefined (zero has no multiplicative inverse).

Regarding infinity, look up the extended real numbers (affine or projective) for ways to include it to the bunch. If you want the reals to remain a complete ordered field, then there's no way to add in infinity.

I have no compulsion to make them a group.

shmoe, go stick your head back in the mathematics textbook dealing with real numbers you just came from and leave it there. One does not need real numbers to see what 360/0 will be if we consider 0 as an approximately tiny number.

There is no point in blasting nonsense about real numbers. Infinity is the result of dividing by an infinitely small number (i.e. approaching 0). There is nothing too complicated about it.

Wow, in one paragraph you accuse me of blasting nonsense about the real numbers and you manage to talk about an "infinitely small number" and you seem to want to include infinity as a real number(?). Oh, the irony.

This isn't about limits, if that's what you are trying to get at.

It originally came up when QQ said 360/0 = 360 and SL correctly pointed out to him that 360/0 was not 360 and was in fact ∞. What do you not understand? You can not claim division by 0 if you want to only consider a real concievable number - the issue of bringing up "real numbers" is nonsense here.

What is a "real concievable number"? The real numbers are nonsense here? What was he talking about then?

The point went right over your head. There IS something mathematically compelling to use 360. The many factors of 360 is the mathematically compelling reason. Now if you said there is no physically compelling reason to use 360, then that would be true. 360 degrees in a circle has no physical meaning.

Human convenience does not dictate mathematical properties. There's a reason that trig functions are defined in terms of radians by mathematicians. 360 degrees is an artificial human construct to make angles things easier to work with (in some cases) and has no bearing at all on the structure or behavior of pi.

I should clarify that "mathematically complelling" to me does not include any choices designed to make life easier for humans. As in there is no mathematically complelling reason to use base 10 over base 6, but there is a mathematically compelling reason to use radians over degrees for defining trig functions (e.g. look at the derivatives of sin, cos).

I have no compulsion to make them a group.

fine, then accept the fact that your real numbers are not the same as the real numbers used by mathematicians everywhere and that whatever statements that may be true in your version of the real numbers have no bearing on the usual ones.

It doesn't affect the rest of the real numbers. What is wrong with infinity? And how can it suddenly break down all the other rules. Show me one rule that it violates.

Wow, in one paragraph you accuse me of blasting nonsense about the real numbers and you manage to talk about an "infinitely small number" and you seem to want to include infinity as a real number(?). Oh, the irony. No. I do not consider infinity to be a real number! That is why I said bringing up real numbers is nonsense.


This isn't about limits, if that's what you are trying to get at.
Yes it is. We need not talk about real numbers. GOOD GOD.



What is a "real concievable number"? The real numbers are nonsense here? What was he talking about then? Who is he? A real number is a number you can concieve of, what is wrong with the adjective I included?



Human convenience does not dictate mathematical properties. There's a reason that trig functions are defined in terms of radians by mathematicians.
360 degrees is an artificial human construct to make angles things easier to work with (in some cases) and has no bearing at all on the structure or behavior of pi. Well I certainly do no believe 360 degrees has any bearing on the structure of pi, but that doesn't mean that the root of 360 degrees in a circle did not have its origin from a mathematically compelling reason. The reason just isn't the same as dealing with other things for which pi was introduced.


I should clarify that "mathematically complelling" to me does not include any choices designed to make life easier for humans. The constuct of pi was to make things easier for humans as well. One can write all the trig functions with another constant so that degrees can be used. That is all pi is, a constant that makes the equations easier for humans.

It doesn't affect the rest of the real numbers. What is wrong with infinity? And how can it suddenly break down all the other rules. Show me one rule that it violates.

You no longer have a field- infinity will not have a multiplicative inverse. It doesn't matter if you agree with the definition of the real numbers that keeps the reals as a field. It's the definition that's been accepted universally and the one that people mean when they say "the real numbers".

Look at the extendend reals (either version). They have thier place in mathematics. Some things get nicer (they are compact) some things get worse (no longer a field), but "the real numbers" will always mean the ones satisfying the complete field axioms.

I suppose there is only one thing worse than Quarkhead, and that is shmoe.

How is that relevent to 360/0 being "not defined"? I was pointing out that the definition is a very good one. So what if it doesn't fit into a group? That doesn't matter most of the time.

Yes it is. We need not talk about real numbers. GOOD GOD.

If you're talking about limits of real numbers you have no choice but to talk about the reals.

QQ and SL both had statements involving 360/0, this is undefined. I see no limit in their posts.

Who is he? A real number is a number you can concieve of, what is wrong with the adjective I included?

"He" is either QQ or SL.

I don't see any difference between a "concievable real number" and a plain old "real number" then, or how it has any bearing on anything at all here.

Well I certainly do no believe 360 degrees has any bearing on the structure of pi, but that doesn't mean that the root of 360 degrees in a circle did not have its origin from a mathematically compelling reason. The reason just isn't the same as dealing with other things for which pi was introduced.

Then there's nothing to argue about here unless we want to delve into what we each mean by "mathematically compelling".

The constuct of pi was to make things easier for humans as well. One can write all the trig functions with another constant so that degrees can be used. That is all pi is, a constant that makes the equations easier for humans.

pi is very 'natural', use something other than radians for sin(x) and it's derivative will no longer be cos(x) but a multiple of it (for example).

How is that relevent to 360/0 being "not defined"? I was pointing out that the definition is a very good one. So what if it doesn't fit into a group? That doesn't matter most of the time.

It is completely relevant. Look at the definition of the reals, see that division by 0 is not defined. I don't know what else you have in mind for "not defined", but it doesn't get any clearer than this.

N/0 is defined as ∞ where ∞ is not a REAL NUMBER

Why the fuck do you keep bringing up REAL NUMBERS?


pi is very 'natural', use something other than radians for sin(x) and it's derivative will no longer be cos(x) but a multiple of it (for example).
See, that is why pi was chosen, because it is mathematically easy.

Before trig, 360 degrees for a circle was mathematically easy.

N/0 is defined as ∞ where ∞ is not a REAL NUMBER
Why the fuck do you keep bringing up REAL NUMBERS?

What else are we talking about? What is 0? What is N? Are these real numbers? No? What then? Or do you just want to talk about these symbols without having any idea at all as to what they are or what rules they obey?

Where do you see N/0 defined as infinity by the way? This would be normal in projectively extended reals (i.e. their 1 point compactification), but I'm not sure this is the context you're refering to, or if you even have a context?

See, that is why pi was chosen, because it is mathematically easy.

Before trig, 360 degrees for a circle was mathematically easy.

This is getting into what I would consider 'mathematically compelling". There are many other reasons why sin and cos are 'natural' functions that come up without even considering any geometrical intrepretation of them eg. their relation to e^x, solutions to a simple differential equation f''=-f, their power series, etc. All the dandy analytical structure we are used to is apparent before you even think about what a radian or even pi is. When you want to have a geometrical meaning, the units of measure for an angle become 'obvious' as this structure is somehow 'natural' and something we'd like to preserve.

What else are we talking about? What is 0? What is N? Are these real numbers? No? What then? Or do you just want to talk about these symbols without having any idea at all as to what they are or what rules they obey?

You are hopelessly lost.

N can be any number you wish it to be. In fact, unless you are talking about integers, N is most likely going to be an approximation. Likewise, 0 is an approximation unless you are talking about integers whereby 0 is directly between 1 and -1. Once you understand this context, that the numbers we are dealing with are approximations, then you must accept that N/0 is infinity.

Now why are the numbers approximations? N was a degree measurement, correct? Any measurement you are going to make is going to have a +/- value which signifies the degree of accuracy. We could say N = 360.04 +/- .01 which means N was measured to be between 360.03 and 360.05.

Furthermore, when we divide N, we need not divide by an integer. So, likewise, the number we are dividing by has a degree of accuracy as well. Both N and 0 exist within a range determined by our measuring capabilities and it just so happens that 0 may be measured in the range of 0 and .01 for instance. That means .000000000000000000000000001 is included in this range as well as even smaller numbers.

It is in that context that N/0 is defined as infinity.

Got it? It's not that hard. Even my TI-89 will tell me that N/0 is infinity.

What the hell are you talking about? In any case 360 and 0 are both integers, so let me say "division by zero is not defined in the integers" so we don't have to get into what on earth you think approximations have to do with anything relevant to this discussion (or how on earth you are trying to reason with them).

Got it? It's not that hard. Even my TI-89 will tell me that N/0 is infinity.

The definitive source- "my calculator said so". Now for the appeal to authority by me, "Maple told me N/0 is "Error, division by zero"". (tongue firmly in cheek)

What the hell are you talking about? In any case 360 and 0 are both integers, so let me say "division by zero is not defined in the integers" so we don't have to get into what on earth you think approximations have to do with anything relevant to this discussion (or how on earth you are trying to reason with them). Well, in that case - you are not working in the real world and you are only talking about the ideal mathematical world. The only thing measured in integers are quantities of objects. Such as: I have 5 apples. I don't have approximately 5 apples, or 4.9 apples, I have -5- apples.

Measurements of degrees, i.e. 360 degree measurement is not an integer. If it is measured, it is an approximation no matter how you slice it. Go shove your head back into your theoretical mathematics book. We have no use for you in the real (as real as this forum is) world.



The definitive source- "my calculator said so". Now for the appeal to authority by me, "Maple told me N/0 is "Error, division by zero"". (tongue firmly in cheek)
Yes, computer languages will warn you when you divide by zero. Here is what MATLAB gives (MATLAB is used by a lot of real world people because of it's vast variety of toolboxes, I believe Maple is more of a stictly mathematical tool):

>> 360/0
Warning: Divide by zero.
(Type "warning off MATLAB:divideByZero" to suppress this warning.)
ans =
Inf
>> 0/0
Warning: Divide by zero.
(Type "warning off MATLAB:divideByZero" to suppress this warning.)
ans =
NaN

See, I get the warning in both instances. But for 360/0 the ANSWER is Infinity and for 0/0 the ANSWER is Not A Number (undefined).

The definitive source- "my calculator said so". I suppose by your logic, I am not to trust my calculator when it says 2+2=4 until I can prove it.

shmoe, go stick your head back in the mathematics textbook dealing with real numbers you just came from and leave it there. One does not need real numbers to see what 360/0 will be if we consider 0 as an approximately tiny number.
0 is most definitely not an approximately tiny number.

End of story.


(Note, just in case you try to argue the point: What is 360/0 if as an approximately tiny negative number? Whooops.)

Well, in that case - you are not working in the real world and you are only talking about the ideal mathematical world. The only thing measured in integers are quantities of objects. Such as: I have 5 apples. I don't have approximately 5 apples, or 4.9 apples, I have -5- apples.

Measurements of degrees, i.e. 360 degree measurement is not an integer. If it is measured, it is an approximation no matter how you slice it. Go shove your head back into your theoretical mathematics book. We have no use for you in the real (as real as this forum is) world.

Your inconsistency is astonishing. In another thread (http://www.sciforums.com/showthread.php?t=47944) you attempted to write a program to "prove" that a right triangle with integer sides couldn't have the other angles as integers (measured in degrees). If you believed that measurements of degrees were not integers (not to mention the sides themselves), than what the hell were you trying to do?

I guess this isn't a "Physics & Math" forum, but a "What Aer declares is the real world" forum? Sorry, I must have missed a memo.

I suppose by your logic, I am not to trust my calculator when it says 2+2=4 until I can prove it.

Calculators or programs are usually designed for ease of use, they are not designed to be a source of mathematical definitions. Maybe you think the constant "e" is defined to be "that thing you get when you enter exp(1) in your calculator", but it's not. Why do you think Matlab warned you about 360/0? I'm willing to make a bet that it's to make the user aware that Matlab is going to replace the symbol "360/0" with "inf", since it's not a universal thing to do but can make a program more robust. The user should be aware that if their program causes a division by zero, this is what matlab will do rather than crash altogether, and they should be aware of potentially "spooky" output if this happens.

0 is most definitely not an approximately tiny number. You are a mathematician as well. I do not expect you to understand.

Approximations happen in reality. Exact numbers happen in theory. Get your head out of your ass.


End of story. I did not ask for the theoretical story.



(Note, just in case you try to argue the point: What is 360/0 if as an approximately tiny negative number? Whooops.)
Negative numbers mean a specific thing. If I know the quantity I am measuring must be positive and I measure it as -.00000000001, then I am going to assume it is 0, not -0. 0 does not have a sign, I would expect a mathematician to know this.

Whoops.

Your inconsistency is astonishing. I've never been inconsistent here.

In another thread (http://www.sciforums.com/showthread.php?t=47944) you attempted to write a program to "prove" that a right triangle with integer sides couldn't have the other angles as integers (measured in degrees). What is wrong with this? That is strictly theory. We wouldn't have any integer 0 sides or angles either. Notice how my sides started at 1 and not 0. Likewise, the angles would have to start at 1 - THAT DOESN'T MEAN YOU CANNOT HAVE AN ANGLE OF 0.1 OR LESS!

This is comparing apples to oranges.


If you believed that measurements of degrees were not integers (not to mention the sides themselves), than what the hell were you trying to do? I proved that in theory, you cannot have integer sides/angles where angles are measured in degrees with a right triangle. The angles will always be non-integers.

Are you trying to tell me that an angle must either be 2 degrees or 3 degrees and cannot be 2.345 degrees?

That is retarded.




I guess this isn't a "Physics & Math" forum, but a "What Aer declares is the real world" forum? Sorry, I must have missed a memo. Well, since you cannot figure out what is the real world, I must take on the responsibility of informing you :rolleyes:




Calculators or programs are usually designed for ease of use, they are not designed to be a source of mathematical definitions. I suppose when my calculator tells me that 0!=1, that is not a definition either. Calculators are programmed with definitions built into them. Geez.

Negative numbers mean a specific thing. If I know the quantity I am measuring must be positive and I measure it as -.00000000001, then I am going to assume it is 0, not -0. 0 does not have a sign, I would expect a mathematician to know this.

Whoops.
You are so out of your league, it's not even funny. Do you really think -0 and 0 are different numbers? (Hint: They aren't.)

Anyway, you're taking the limit of

360/x

when x goes to 0 from the right (i.e. from the positive side of 0)

lim x -> 0+ 360/x = ∞

and using that as the definition of 360/0 because 360/0 is undefined, if 360 is a real number, and / is standard division.

You have not justified this, and I even showed why it's a bad idea, since

lim x -> 0- 360/x = -∞

Your bullshit comment about 360/0 being infinity was wrong. You can define a new binary operator on something like the reals extended with infinity in which "Aer's new division operator" is defined when the second operand is zero as being infinity, but [I]that's not the same thing as 360/0 being infinity.

You. Are. Wrong.

What is wrong with this? That is strictly theory. We wouldn't have any integer 0 sides or angles either. Notice how my sides started at 1 and not 0. Likewise, the angles would have to start at 1 - THAT DOESN'T MEAN YOU CANNOT HAVE AN ANGLE OF 0.1 OR LESS!

This is comparing apples to oranges.

I get it. The only time theory is allowed is when you post it. Are you the apple or the orange?


I proved that in theory, you cannot have integer sides/angles where angles are measured in degrees with a right triangle. The angles will always be non-integers.

There was a reason I put "prove" in quotes, you only checked up to a finite bound, and ignored any possible internal rounding 'problems' with matlab (not strictly problems, but just how it deals with arithmetic).


Are you trying to tell me that an angle must either be 2 degrees or 3 degrees and cannot be 2.345 degrees?

I have no idea where this came from, but it doesn't seem to be in response to anything I wrote. I was simply questioning why you would bother to "prove" that there couldn't be a triangle with whole sides and integer angles if you already believed that the angles couldn't be integers since they were approximations. I mean, why the extra effort?

Oh, right. You're allowed to post theory, but no one else is.

Well, since you cannot figure out what is the real world, I must take on the responsibility of informing you :rolleyes:


When have I ever made any claims that anything I said was "the real world"? Please point them out to me.

I suppose when my calculator tells me that 0!=1, that is not a definition either. Calculators are programmed with definitions built into them. Geez.

They are, but they sometimes make sacrifices for robustness. Do you think that Maple isn't programmed with any definitions?

Negative numbers mean a specific thing. If I know the quantity I am measuring must be positive and I measure it as -.00000000001, then I am going to assume it is 0, not -0. 0 does not have a sign, I would expect a mathematician to know this.

Whoops.

You are so out of your league, it's not even funny. Do you really think -0 and 0 are different numbers? (Hint: They aren't.)
What part of my response did you not understand? I suspect it was this part where I clearly said 0 does not have a sign. Exactly how does that mean that -0 and 0 are different? I told you that there was no difference!

You are out of your league when it comes to reading comprehension..

Anyway, you're taking the limit of I know it is a limit, that is what I've said all along!

We are working with limits when talking about approximate numbers.

N/0 is defined as infinity unless you are talking strictly about integers. It is as simple as that.

I get it. The only time theory is allowed is when you post it. Are you the apple or the orange?
You are confused again. Theory needs to be applicable to what you are applying it to. Saying that N and 0 must be defined as integers is where your argument breaks down because they need not be integers and furthermore may only be approximations. Get real.

There was a reason I put "prove" in quotes, you only checked up to a finite bound, and ignored any possible internal rounding 'problems' with matlab (not strictly problems, but just how it deals with arithmetic). Yes, I agree it wasn't a formal proof, but any more than 10,000 would have taken more than the couple of seconds of computation my computer could handle. I could have written a more efficient program to skip similiar triangle calculations but a quick and dirty check up to 10,000 was all I cared to do.

I have no idea where this came from, but it doesn't seem to be in response to anything I wrote. I was simply questioning why you would bother to "prove" that there couldn't be a triangle with whole sides and integer angles if you already believed that the angles couldn't be integers since they were approximations. I mean, why the extra effort? This is about as retarded as it gets. A mathematical proof of integer relations is different from measuring.

What is wrong with this? That is strictly theory.

I proved that in theory, you cannot have integer sides/angles where angles are measured in degrees with a right triangle. The angles will always be non-integers.

You absolutely, positively did no such thing. Your non-recognition of "real" as an adjective in reference to numbers and this ludicrous statement leads me to believe that you've actually not been exposed to mathematical proofs much.

Here are two uttely destroying problems with your "proof":

1) You test combinations of side lengths ranging from 1 to 10000. That leaves infinitely many cases unaccounted for.
2) You use numerical approximations of acos and pi (yes, you do), meaning that your test is not even to be trusted for the incredibly few instances you've tried. Furthermore you compare floating point numbers (the equality tests) after doing approximate calculations, something every CS student learns the hard way.

This sums to you having proved exactly nothing at all.

I suppose when my calculator tells me that 0!=1, that is not a definition either. Calculators are programmed with definitions built into them. Geez.
That's not a definition. It's a (true) inequality.


Depending on the sofistication of your calculator, it will most probably also tell you that (0.000000001)^100 = 0. Do you think this is true, too?

lim x -> 0+ 360/x = ∞

and using that as the definition of 360/0 because 360/0 is undefined, if 360 is a real number, and / is standard division.

You have not justified this, and I even showed why it's a bad idea, since

lim x -> 0- 360/x = -∞

Your bullshit comment about 360/0 being infinity was wrong. You can define a new binary operator on something like the reals extended with infinity in which "Aer's new division operator" is defined when the second operand is zero as being infinity, but [I]that's not the same thing as 360/0 being infinity.

You. Are. Wrong.

Funkstar, you clearly missed the context of everything here, QQ was dividing 360 by numbers. He was trying to show how 360 was a factor of every integer. schmoe took this to mean that angles can only be divided by integers, which is not true. An angle can be divided by any number you want. When you start dividing by numbers less than 1, it is the same as multiplying by the inverse of that number which would be greater than 1. So when 0 is included in the following list, division by 0 must be approached as the limit of x as x->0+ of 360/x. What is so difficult here?

As QQ posted it:

360/0 = 360
360/1 = 360
360/2 = 180
360/3 = 120
360/4 = 90
360/5 = 72
360/6 = 60
360/7 = 51.42857143
360/8 = 45
360/9 = 40

We are working with limits when talking about approximate numbers.

No. Even this is wrong. And we're not doing approximate numbers.

N/0 is defined as infinity unless you are talking strictly about integers. It is as simple as that.
This is still wrong. If we're talking reals, x/0 is still undefined.

You're. Wrong.

You absolutely, positively did no such thing. Your non-recognition of "real" as an adjective in reference to numbers and this ludicrous statement leads me to believe that you've actually not been exposed to mathematical proofs much. Sorry funkstar, but your blather has no relevance here. I already said that it was not a formal proof.



There was a reason I put "prove" in quotes, you only checked up to a finite bound, and ignored any possible internal rounding 'problems' with matlab (not strictly problems, but just how it deals with arithmetic).
Yes, I agree it wasn't a formal proof, but any more than 10,000 would have taken more than the couple of seconds of computation my computer could handle. I could have written a more efficient program to skip similiar triangle calculations but a quick and dirty check up to 10,000 was all I cared to do.


I know the difference between a formal proof and what I did - I've taken plenty of high level math courses. I already stated that calling it a "proof" was a misnomer.

No. Even this is wrong. And we're not doing approximate numbers. YOU ARE NOT USING APPROXIMATE NUMBERS. I am. You are only working with integers, I am not.

I realize you are a mathematician and therefore you jumped all over this thread to strut your stuff, but you are simply wrong. As a mathematician, I suspect you have no concept of degree of accuracy and that almost all numbers used in any real world calculation is an approximation with the exception of "counted" quantities. If you have 5 apples in your hands - that is not an approximation. But if you were to weigh those same 5 apples on a scale, that weight will always be approximate.

Funkstar, you clearly missed the context of everything here, QQ was dividing 360 by numbers. He was trying to show how 360 was a factor of every integer.

I know perfectly well how this came about.

schmoe took this to mean that angles can only be divided by integers, which is not true.

He didn't. He took exception to your claim that 360/0 is infinity, because it isn't. It's undefined.

An angle can be divided by any number you want. When you start dividing by numbers less than 1, it is the same as multiplying by the inverse of that number which would be greater than 1. So when 0 is included in the following list, division by 0 must be approached as the limit of x as x->0+ of 360/x. What is so difficult here?

The difficulty is that it's just not true. You can't even use the limit

lim x -> 0 360/x != infinity

because

lim x -> 0+ 360/x != lim x -> 0- 360/x

and both are limits of 360/x when x goes to zero.

That's all there's to it. 360/0 is not infinity.

You are only working with integers, I am not.

Certainly not.

If x=0 is a real, 360/x is undefined.

He didn't. He took exception to your claim that 360/0 is infinity, because it isn't. It's undefined. for integers. I've never claimed otherwise. And it was not myself who claimed 360/0 = infinity, it was superluminal. And it was superluminal that he took exception to, not me. Get your facts straight if you want to claim that you know how all this came about.

Your post below is evidence that you have no clue how it all came about:

The difficulty is that it's just not true. You can't even use the limit

lim x -> 0 360/x != infinity

because

lim x -> 0+ 360/x != lim x -> 0- 360/x

and both are limits of 360/x when x goes to zero.

See, you are still trying to approach 0 from the negative end! HA! Nice try though, it truely is the strongest argument you have going for you. Keep hitting on it some more. Maybe I'll give up telling you that the negative end is irrelevant for the purpose brought up in this thread. Probably not though.

Sorry funkstar, but your blather has no relevance here. I already said that it was not a formal proof.

It's not even a good approximate test. You make the rookie mistake of comparing floating point numbers.

Certainly not.

If x=0 is a real, 360/x is undefined.

what is 360/N where N=.0005 +/- .0005 degree of accuracy?

See how measured quantities cannot be arbitrarily defined as real? I suspect your answer will be no because you are a mathematician.

Who cares about measured quantities?

360 divided by 0 is not infinity.

You make the rookie mistake of comparing floating point numbers.

It was good enough for the accurarcy of MATLAB and the limit of 10,000 that I used. I understand when results become inaccurate because of computer limitations. In fact, MATLAB would have warned me of any such results with warning messages. I had that covered :D

what is 360/N where N=.0005 +/- .0005 degree of accuracy?

See how measured quantities cannot be arbitrarily defined as real? I suspect your answer will be no because you are a mathematician.
Holy crap, you really don't know what a "real" is, do you?

"I've taken plenty of high level math courses."

Yeah. Sure you have.

Who cares about measured quantities?

360 divided by 0 is not infinity.
That is entirely my point. As a mathematician, you have no conceptual clue as to why N/0 is infinity when you are talking about real world numbers. Again, integers clearly do not apply.

Holy crap, you really don't know what a "real" is, do you?

"I've taken plenty of high level math courses."

Yeah. Sure you have.
A real is any rational or irrational number.

Yes, I have taken plenty.

This is about as retarded as it gets. A mathematical proof of integer relations is different from measuring.

Who "measured" anything in this thread? Were you peeking in QQ's window as he played with cardboard cutouts of triangles?

schmoe took this to mean that angles can only be divided by integers, which is not true.

I guess I'm schmoe, but I didn't do what you're claiming here. My hope of restricting N/0 to being integers was to divert the course from your insane ramblings about approximations that doesn't appear to have any relevance here. Even by your own "measuring" rantings, what is 0 in QQ's post measuring? care to explain how it's somehow not an integer?

Do you think there are 360 degrees in a circle or is it 360+/- 0.01?

I guess I'm schmoe, but I didn't do what you're claiming here. Sorry for making your nickname German - it is just my nature.


My hope of restricting N/0 to being integers was to divert the course from your insane ramblings about approximations that doesn't appear to have any relevance here.
I realize you don't believe it to have any relevance, but it is relevant. What else can I say?


Even by your own "measuring" rantings, what is 0 in QQ's post measuring? care to explain how it's somehow not an integer? Like I said before, he only showed the result of the integer divisions - why does that make any angle you divide have to be divided by an integer?



Do you think there are 360 degrees in a circle or is it 360+/- 0.01?
The number of degrees in a circle is defined as 360. Dividing this angle by 1/2 is the same as multiplying it by 2. Dividing by 1/100 is the same as multiplying by 100. Dividing by 1/10000 is the same as multiplying by 10000. See the trend? It goes to infinity.

Holy shit, imagine that.

A real is any rational or irrational number.

Good!

Now is division defined for reals? Yes, it is, except when the second operand is zero. Well, does it at least have a unique limit, that we can use instead? No, it does not.

What does this mean? It means that 360/0 is not infinity. Now, even if we extend the reals to include +/- infinity, it still doesn't make 360/0 = +infinity.

Good!

Now is division defined for reals? Yes, it is, except when the second operand is zero. Well, does it at least have a unique limit, that we can use instead? No, it does not.

What does this mean? It means that 360/0 is not infinity. Now, even if we extend the reals to include +/- infinity, it still doesn't make 360/0 = +infinity.

How about you answer my question:

what is 360/N where N=.0005 +/- .0005 degree of accuracy?

Do you know how to do such a calculation? I know I had to do such mundane calculations in chemistry lab.

Sorry for making your nickname German - it is just my nature.

No problem, for some reason it's a common thing to do.

Like I said before, he only showed the result of the integer divisions - why does that make any angle you divide have to be divided by an integer?

It doesn't, I never said it did. So, you seem to agree he was talking about integer divisions, what then is the approximation in the attempted 360/0?

The number of degrees in a circle is defined as 360. Dividing this angle by 1/2 is the same as multiplying it by 2. Dividing by 1/100 is the same as multiplying by 100. Dividing by 1/10000 is the same as multiplying by 10000. See the trend? It goes to infinity.

Holy shit, imagine that.

Notice everything you've got there are real numbers (rational if you prefer). 100, 1/100, 10000, 1/10000 and you're defining, or at least thinking about it in this way, "division" by a number x as "multiplication by the multiplicative inverse of x" (no problems here, this is a fine way to think of division).

The problem is when you want to divide by 0, it doesn't have a multiplicative inverse. Everything you are working with in your approximations are rational numbers here. Can you tell me the rational number that when multiplied by 0 gives you 1? I'm sure you know this can't be infinity for two reasons, it's not a rational number and trying to define 0*infinity=1 is not going to play well with your limit idea. You can reject the first reason if you want to talk about things that aren't rationals, but the second is going to bite you in the ass.

Aer,

Sorry I said 360/0 was infinity. Deep down I knew that was wrong, but not being a mathemetician, I was unforgivably loose with such a thing. N/0 is undefined, not infinity. I'd listen to funkstar if I were you. Other operations involving infinity do not work if you define N/0 as infinity. It's a mess. It's simply undefined. That's why compilers and such say "Illegal operation" or something like that when you try it.

How about you answer my question:

what is 360/N where N=.0005 +/- .0005 degree of accuracy?

Do you know how to do such a calculation? I know I had to do such mundane calculations in chemistry lab.
360/N is in [360,000 ; +infinity[. Note the exclusion of infinity in the interval. Here's one for you:

What is 360/N where N=0.0000 +/- 0.0005 ?

Anyway, who cares? It doesn't make 360/0 any more defined...

shmoe,

Yep.

Notice everything you've got there are real numbers (rational if you prefer). 100, 1/100, 10000, 1/10000 and you're defining, or at least thinking about it in this way, "division" by a number x as "multiplication by the multiplicative inverse of x" (no problems here, this is a fine way to think of division).

The problem is when you want to divide by 0, it doesn't have a multiplicative inverse. This is your problem. You are saying a number must either be .0001 or .00001 or some other finite value, but if you don't know and cannot know, then how is one to do any division? What is 360/N when N is measure as .0001 with an accuracy of +/- .0001? I'll give you a hint, you have to compute two numbers such that your answer to 360/N fits within a range. And it's rather simple to do, so I do not understand why you are avoiding it.

N/0 is undefined, not infinity. I'd listen to funkstar if I were you. I did listen to funkstar and I agree that N/0 is undefined when 0 is an integer value.

Now, when measuring something, the range is always in the range of real numbers, but there is no upper bound on real numbers now is there? In practise, we take this upper bound to be infinity because there is a point in which the numbers are much greater than the scope of what is being analyzed. Any numbers greater than this "scope" is infinity.

In fact, for air flow boundary layer problems, infinity is often a meause of a few milimeters. You can hold infinity in your hand :D




Other operations involving infinity do not work if you define N/0 as infinity. It's a mess. It's simply undefined. That's why compilers and such say "Illegal operation" or something like that when you try it. What are you talking about? The mathematical language I have on my computer defines N/0 as infinity. My calculator defines N/0 as infinity.

0/0 on the other hand is clearly undefined.

360/N is in [360,000 ; +infinity]. Note the exclusion of infinity
in the interval.
Maybe your notation is funny, but how is infinity excluded? 360,000 is included in the interval as the lower bound, so should infinity be included as the upper bound. I agree that it doesn't make sense to say "infinity is within the interval" but you couldn't have calculated the infinity upper bound if you didn't define 360/0 as infinity.


Here's one for you:

What is 360/N where N=0.0000 +/- 0.0005 ?

Anyway, who cares? It doesn't make 360/0 any more defined...
[360,000 ; +infinity] and [-360,000 ; -infinity] Would you care to share a real world example in which what you are dividing with can be positive and negative? I'm not saying it is impossible, I just don't have an example right off the top of my head. The asymptotic nature of the solution is what usually requires it either be positive or negative.

Aer,

I did listen to funkstar and I agree that N/0 is undefined when 0 is an integer value.
Ok.

Now, when measuring something, the range is always in the range of real numbers, but there is no upper bound on real numbers now is there? In practise, we take this upper bound to be infinity because there is a point in which the numbers are much greater than the scope of what is being analyzed. Any numbers greater than this "scope" is infinity.

In fact, for air flow boundary layer problems, infinity is often a meause of a few milimeters. You can hold infinity in your hand
Not sure what you are getting at here.

What are you talking about? The mathematical language I have on my computer defines N/0 as infinity. My calculator defines N/0 as infinity.
That's wierd. Every calculator I ever owned displays an E or -E- when I divide by zero, and any code I've ever written displays some form of illegal operation flag when I stupidly allow a zero in the denominator.

0/0 on the other hand is clearly undefined.
Ha! No, this is indeterminate!

That's wierd. Every calculator I ever owned displays an E or -E- when I divide by zero, and any code I've ever written displays some form of illegal operation flag when I stupidly allow a zero in the denominator.
I suspect you have a pocket calculator that is basically as dumb as a rock (or a phone calculator, I just tried my phone, it gives me an error). Try a TI-89.


Ha! No, this is indeterminate!
I hate you.

I hate you.

LMAO! :D

My daughter has a TI-89, she's getting it for me now...

Update: Ok, it's a TI-86 and it says "Error 02 Div by Zero" My HP gives an error also. Not &infin;

My daughter has a TI-89, she's getting it for me now...

Update: Ok, it's a TI-86 and it says "Error 02 Div by Zero"
Well, I cannot speak for a TI-86. I suspect the TI-86 doesn't have an infinity symbol on it neither? My TI-89 has a green infinity symbol, I forget where though as I don't have it on me at the present.

If you'll trust my MATLAB skills, here is the result it gave:

>> 360/0
Warning: Divide by zero.
(Type "warning off MATLAB:divideByZero" to suppress this warning.)
ans =
Inf

Gives both a warning incase you didn't intend to divide by zero, and the result that it is infinity.

I'll bet you a dollar that it dosen't show up when you divide N by zero.

This is your problem. You are saying a number must either be .0001 or .00001 or some other finite value,

They do. Numbers don't change or move. Real (or rational or integer) "numbers" are all "finite".

but if you don't know and cannot know, then how is one to do any division? What is 360/N when N is measure as .0001 with an accuracy of +/- .0001? I'll give you a hint, you have to compute two numbers such that your answer to 360/N fits within a range. And it's rather simple to do, so I do not understand why you are avoiding it.

I'm not avoiding anything, I just don't see the relevance. Giving bounds on 360/N knowing some tolerance on N does not in any way make division by zero defined. If there was the possibility that N=0 was in your interval, the answer would include a statement about the question being undefined if N=0. Anytime you see a mathematician divide by an unknown x (and I'd hope a physicist as well, though I make no claims about them), they will have made sure that x is not zero, or treated this possibility seperately.

I'll bet you a dollar that it dosen't show up when you divide N by zero.
Deal, I'll take a picture of it and post it tomorrow.

I even bet you get error 260.

I'm not avoiding anything, I just don't see the relevance. Giving bounds on 360/N knowing some tolerance on N does not in any way make division by zero defined. If there was the possibility that N=0 was in your interval, the answer would include a statement about the question being undefined if N=0. Anytime you see a mathematician divide by an unknown x (and I'd hope a physicist as well, though I make no claims about them), they will have made sure that x is not zero, or treated this possibility seperately.
You are talking about the theoro-world. When dealing with theory, a number is always precise as there is no range for error. But even in some instances scientists do us the result 1/0=infinity.

Assuming James R is a qualified scientist or whatever, here is an example:
For the photon m=0 and the v in the gamma is equal to c, so gamma goes to infinity and m is zero. What is zero times infinity? In this case, it is a finite number, but the equation doesn't tell you that. How did he arrive at the conclusion that gamma is infinity you ask? well 1/sqrt(1-v/c) as v approaches c is 1/0 = infinity.

I even bet you get error 260.
2nd bet noted. So are we at $2 now?

Sure.

Maybe your notation is funny, but how is infinity excluded? 360,000 is included in the interval as the lower bound, so should infinity be included as the upper bound.

Infinity isn't usually considered a number. And in any case, 360/0 is still not infinity, so there's no value for N in the given interval, in which 360/N is infinity.

I agree that it doesn't make sense to say "infinity is within the interval" but you couldn't have calculated the infinity upper bound if you didn't define 360/0 as infinity.

Well, the division is continuous arbitrarily close to zero, and the limit from the right is well-defined. I don't need 360/0 to be infinity to calculate the limit from the right.

[360,000 ; +infinity] and [-360,000 ; -infinity]

See, that doesn't work. Which N in [-0.0005 ; 0.0005] allows 360/N to be +/- infinity? Infinity is not in range, even if you include the discontinuity point. So +/- infinity should not be included...

Would you care to share a real world example in which what you are dividing with can be positive and negative? I'm not saying it is impossible, I just don't have an example right off the top of my head. The asymptotic nature of the solution is what usually requires it either be positive or negative.
How about, say, charge?

Aer,

In Matlab then, Inf clearly stands for "INFucking possible" Yes?

How about, say, charge? Charge is a quantized quantity, is it not? Anyway, what are you measuring as far as charge is concerned that you don't know if it is going to be positive or negative? I suspect if you are unable to tell within a degree of accuracy that you must conclude that the net charge is neutral, for all intents and purposes anyway.

matlab will also tells me that gamma(1000)=inf, does that mean there are only finitely many integers?

Seriously, don't use a program as your source for mathematical definitions.


Assuming James R is a qualified scientist or whatever, here is an example:

I'm willing to bet that James R understands the limits involved and can put things on a rigorous footing and that physicists have carefully explored the relevant behavior at the boundaries of where these equations are valid.

I'm also willing to bet you a coke that james R doesn't think that division by zero is defined in the way you are claiming it is. Are you willing to take him as a source that will shut you up?

shmoe:

Anytime you see a mathematician divide by an unknown x (and I'd hope a physicist as well, though I make no claims about them), they will have made sure that x is not zero, or treated this possibility seperately.

If you write code, then you must always disallow division by zero.

...

for(i = -10; i <= 10; i++)
{

if(i == 0) k = 0; //or some other value that indicates div by zero
else k = 2/i;
}

...

Aer,

In Matlab then, Inf clearly stands for "INFucking possible" Yes?
very good question. Let's see here:

>> Inf-1
ans =
Inf
>> Inf^2
ans =
Inf
>> Inf*0
ans =
NaN

Ahh, Inf*0 is 1/0*0 which is 0/0 which is undefined (i.e. NaN).

Your assertion was a good one, but not a correct one :D

Aer,

You stand to get $2.00 and a coke if we're wrong.

matlab will also tells me that gamma(1000)=inf, does that mean there are only finitely many integers?

Seriously, don't use a program as your source for mathematical definitions.
Thats because the solution to gamma(1000) is well over the scope of matlab's capabilities, here is a program to prove it:

>> i=100; e=0;
while(e~=Inf)
e=gamma(i); i=i+1;
end
>> i
i =
173
>> gamma(173)
ans =
Inf
>> gamma(172)
ans =
Inf
>> gamma(171)
ans =
7.2574e+306


Not sure why it went to 173 when gamma(172) was Inf, but I digress.
(Edit: OH! I put the i=i+1; on the wrong side, oh well)


I'm willing to bet that James R understands the limits involved and can put things on a rigorous footing and that physicists have carefully explored the relevant behavior at the boundaries of where these equations are valid. I too understand the limits involved. I've never said it is anything other than a limit. It is just a definition from the limit case.


I'm also willing to bet you a coke that james R doesn't think that division by zero is defined in the way you are claiming it is. Are you willing to take him as a source that will shut you up? James R will never shut me up :D

Anway, I don't get what your problem is anyway. 1/0 is defined as infinity for convience. You made the argument earlier that pi was defined for convience. Now I know these are completely different situations. But they are nevertheless mathematical definitions.

Ah, Aer... the ultimate arrogant poster, who freely admits his lack of knowledge in specialised topics, but still proceeds to lambast and insult those who dare to correct his uneducated opinions. :rolleyes:

Some come here to learn... but some come just to fight.
They just want to win - they really don't care if they're wrong or right.

Ah, Aer... the ultimate arrogant poster, who freely admits his lack of knowledge in specialised topics, but still proceeds to lambast and insult those who dare to correct his uneducated opinions. What is uneducated about anything I have said? Nothing I have claimed is in contention except N/0 = Inf


Some come here to learn... but some come just to fight. I see you have nothing to say on this topic except initiate conflict. Who is really here to fight and who is here to learn?


They just want to win - they really don't care if they're wrong or right. Nothing shmoe or funkstar have said makes me think that my position is wrong. They just misunderstand my position which is apparent when they try to tell me what I think.

Also Pete, whenever I've offered my opinion on a subject in which my knowledge is limited, I have freely admitted such before hand. However, I was just stating the opinions I've heard from people I at least thought were qualified to know what they are talking about.

Ok ....I just got online and have read the fluff and flurry I seem to have generated with my ignorance. This is not unusual for me I might add...ha.


Just for the record:
My intent with 360/0 was on the somewhat naive and simplistic notion that to divide something with nothing leaves the something unchanged.
I was exploring the notion that each digit of pi was a percentage of a 360 degree spiral. As the spiral reduces in diameter to infinity a pattern may form.

Any way I realised in the end that I have no where near enough the math ability to draw such a thing. I can visualise it but can not construct it mathematically.

My intent with 360/0 was on the somewhat naive and simplistic notion that to divide something with nothing leaves the something unchanged. Oh my. I must say, this is just as good as the light doesn't travel argument - possibly better!

QQ,

The plot looks like this:

http://laserwireless.net/Diagrams/pi_curve.bmp

so in laymans terms how does attempting to divide something with nothing leave that something changed. Notice I am not using mathematics in my question which is probably why I have the problem to start with.

I have a rock and I am attempting to divide it with nothing. How does this change the rock?

QQ,

The plot looks like this:

http://laserwireless.net/Diagrams/pi_curve.bmp

Thanks for that however To plot my solution one has to start with a spiral....or at least an infinite number of circles reducing. The pi digit being a percentage of the circumfurence of each circle [spiral] reducing to infinity.

sheesh!! almost impossible to describe.... :mad:

BTW the fact that zero appears in the pi digit sequence renders the idea unfeasable any way.....

so in laymans terms how does attempting to divide something with nothing leave that something changed. Notice I am not using mathematics in my question which is probably why I have the problem to start with.

I have a rock and I am attempting to divide it with nothing. How does this change the rock?


ahhh!!! hang on a miniie,

So i want to divide a rock so that it has zero parts.....maybe thats the impost.....

Umm... it dosen't? In math when you divide something you are asking "How many equal parts P of N are there? (N/P)". With a rock, you are asking "How many pieces will I get if I break it N times? Well, breaking it zero times leaves you having done no operation on it. Right?

but it could be concluded that you would get an infinite number of zero parts. Thus 360/0 can = infinity and yet no action has occurred to split the rock.....so this in philosophy would be an endless paradox. I guess in the end it comes down to intent.
I was attempting to find a percentage of 360 degrees and zero would I guess give me 0% as an infinite % doesn't make sense.
So maybe the intent limits the question

Asking :
What percentage of 360 is zero?

Zero.

QQ, "dividing by nothing" is a nonsense construct. This is the very point that shmoe and funkstar make, but they fail to realize that in practicality N/0 is defined as dividing N by a very small number. You are not in fact dividing by "nothing".

To illustrate the point. When you divide by 1/2, you are multiplying by 2. So you are in fact talking about 2 rocks instead of 1 if you wish to think of it that way. when you do the so-called "divide by zero" you are multiplying by infinity, so you are left with infinity rocks. Get it? I know the math nerds aren't going to like it, but that is how N/0 is defined.

Here:

http://www.laserwireless.net/Diagrams/pi_2.bmp

Here:

Cool.

(I see nothing)

Aer:

You seem to be wanting to claim that, since N and 0 are "approximations", N/0 must be infinity.

Then answer this. Suppose N = 20.000000 +/- 0.000001. (I am including the uncertainty explicitly.)
Suppose, further, than x = 0.0 +/- 0.1

Question: What is your value for N/x, including the uncertainty?

Next, suppose that x = 0.000000 +/- 0.000001. What is the value of N/x now?

Suppose x is zero, plus or minus 0.[1 hundred million zeros]1. What is the value of N/x?

Next, suppose that x = 0.000000 +/- 0.000001. What is the value of N/x now? I already answered a similar question that funkstar posed. Keep reading.

Here it is so you don't have to go searching:


Here's one for you:

What is 360/N where N=0.0000 +/- 0.0005 ?

Anyway, who cares? It doesn't make 360/0 any more defined...


[360,000 ; +infinity] and [-360,000 ; -infinity] Would you care to share a real world example in which what you are dividing with can be positive and negative? I'm not saying it is impossible, I just don't have an example right off the top of my head. The asymptotic nature of the solution is what usually requires it either be positive or negative.

"How many equal parts P of N are there? (N/P)". With a rock, you are asking "How many pieces will I get if I break it N times? Well, breaking it zero times leaves you having done no operation on it. Right?

It may be better to look at it as:

If I have N objects, and I split them into groups of P objects, how many groups will there be? (e.g. If I have 10 objects, and break them into groups of 2, there will be 10/2 = 5 groups.)

If I have 10 objects, and break them into groups of zero, how many groups will there be?

Math nerds... *snort*

Go look again at my rendering of QQ's pi spiral. It's a wierd pseudo-polar radar thingy in excel...

Looks to me like one big snail got caught in a spider web.

I already answered a similar question that funkstar posed. Keep reading.

I read your response to funkstar.

You seem to be backing down from your initial statement, adding in a qualification that "only positive answers are allowed", in effect.

Is that a correct summary of your position? If not, please explain.

You seem to be backing down from your initial statement, adding in a qualification that "only positive answers are allowed", in effect.

Is that a correct summary of your position? If not, please explain. Well, you are confused about what I am refering to. In the purposes of this thread, the answer can only be positive infinity because we are clearly approaching zero from the positive side. I qualified this later to say that if I knew a measurement must be positive, but the accuracy of my measuring device was slightly miscalibrated and measured a very small negative number - then I would still conclude that it is approximately zero as approaching from the right hand side. Now I added a little more explaination to what I mean because I am sure you can handle it - those other bozos, I am not so sure about.

Hey,

I won't post the new plot, but I just found a nifty polar plotting add-in for excel. Works good.

Hey Sl great now use the digits of pi as a percentage in sequence instead of the table I posted....hmmmmm...is that possible

QQ, pi = C/D where C is the circumference of a circle and D is the diamter of the circle. It doesn't have anything to do with 360 degrees in a circle.

QQ,

Not sure what you want...?

And Aer is right. 360 is arbitrary.

As a side note, I want to create a rectangle. So I take a circle with a diameter down the center. I slice the circle perpendicular to the diamter line. The resulting 4 pieces from the slice (2 identical pieces from the circumfernce (pieces can be straightened), 2 identical pieces from the diameter) are used to create my rectangle. What is the area of my rectangle?

QQ, pi = C/D where C is the circumference of a circle and D is the diamter of the circle. It doesn't have anything to do with 360 degrees in a circle.
as I said earlier it is way to hard to describe my reasoning. so I wont bother at the moment.
However what i will share is that the center of the circle is an undefinable infinite point of reduction......The interest in it stems from the notion that to find the center of concentrated space time is an infinite task of constant reduction.

It seemed to me that because Pi is an infinitly resolving value [ the resolution goes on infinitely] that it may have something to show us about the finding of our center of spacetime...

sorry if this is confusing......maybe later I will be able to clarify my propositions a bit better...

I guess the first thing you assumed is that spacetime is a 2D circular plane?

QQ,

Not sure what you want...?

And Aer is right. 360 is arbitrary.

correct but a circle isn't

A circle is not arbitrary in the context that it is different from a square? Maybe. ..it's hard to think like you.

I guess the first thing you assumed is that spacetime is a 2D circular plane?

Nope.....but it is useful to take a 2 dimensional slice of a 3d sphere

A circle is not arbitrary in the context that it is different from a square? Maybe. ..it's hard to think like you.

shit man I find it hard to think like me...can't imagine how hard it would be for someone else to think like me..... :D

OK - so spacetime is a 3D sphere. Suppose even if this is the case, what causes me to choose a 2D slice of spacetime that goes through the center of the sphere?

can't go through the center only towards the center.

OK - what prevents me from choosing a 2D slice of spacetime that goes through the center of the sphere?

sorry I have nothing more to add....all I am doing is adding to the confusion.....so I'll do some sorting out and get back

OK - what prevents me from choosing a 2D slice of spacetime that goes through the center of the sphere?

Do you have any idea how you can go through the center of space time when getting there is an infinite propostion....think of falling into a black hole as an analogy......any way I'm out of here

Perhaps the answers to all your questions exist in this black hole.

any way I'm out of here Nice talking to you.

Ok, Aer.

Then could you please answer my questions about the value of N/x, assuming that negative "approximations" aren't allowed?

For example, if N can range from 19.9999 to 20.0001, and x can range from 0 to 0.0001, then what are the possible values of N/x?

Is it therefore true to say that N/0 is infinite, using your argument that the N and the zero are approximations?

Ok, Aer.

Then could you please answer my questions about the value of N/x, assuming that negative "approximations" aren't allowed?

For example, if N can range from 19.9999 to 20.0001, and x can range from 0 to 0.0001, then what are the possible values of N/x?

Is it therefore true to say that N/0 is infinite, using your argument that the N and the zero are approximations?
Well congratulations, you finally got around to asking a well-posed question.

Just as you might have imagined, since the values of N and x can range, the solution to N/x is going to be a range.

This range is found by calculating:
19.9999/.0001 = 199999 for the lower bound
20.0001/0 = ∞ for the upper bound

Notice how N/0 must be defined as infinity? Neat how that works isn't it. :rolleyes:

If 1/2 = 0.5 then 0.5 * 2 = 1

If 37.2/4.8 = 7.75 then 7.75 * 4.8 = 37.2

If 1/0 = &infin; then &infin; * 0 = 1 ???

or,

If 45.678/0 = &infin; then &infin; * 0 = 45.678 ???

How's that?

If 1/0 = &infin; then &infin; * 0 = 1 ???

It is for this reason that &infin; is not defined as a real number.
&infin; * 0 = 1 is incorrect.
&infin; * 0 = undefined is correct.

Remember, that &infin; is 1/0, so,
&infin; * 0 = 1/0 * 0 = 0/0 = undefined.


or,

If 45.678/0 = &infin; then &infin; * 0 = 45.678 ???

How's that?
The reason &infin; * 0 is undefined is because the solution can be any range of numbers from 0 to &infin; depending on the order of magniutde of the accuracy of your numbers.

I've been reading a bunch of math sites, and they think you are wrong. I will go eat them with my new avatar for you. Grrrr (http://www.laserwireless.net/Diagrams/Dog Growl V2.mp3)

I've been reading a bunch of math sites, and they think you are wrong. I will go eat them with my new avatar for you. Grrrr (http://www.laserwireless.net/Diagrams/Dog Growl V2.mp3)
What math sites are you referring to? I'd really like to visit these math sites that think.

Anyway, I am sure I will agree with anything they say if they are a legitimate math site because I already have an idea of what they are going to refer to when saying that dividing by 0 is undefined. That is, when refering to 0 as an integer value, not an approximation, then division by 0 is undefined. I mentioned this about 5 pages back :D

I know. Whatever. If your zero is an approximate zero (which isn't zero) then 1/~0 has a finite value and is not infinity. You are wrong no matter how you look at it. Zero is 0. It's not an approximate concept.

I know, you've been over this...bla...bla...bla. There's no other definition of zero. Unless it's spelled AER. :D ;)

<center>SILENCE.</center>

I know. Whatever. If your zero is an approximate zero (which isn't zero) then 1/~0 has a finite value and is not infinity. I never said that it was anything other than a limit. The limit goes to infinity, yes? :)

You are wrong no matter how you look at it. Zero is 0. It's not an approximate concept. Zero is only 0 when you are talking about integers. The only way you know something is exactly zero is when you are dealing with "counting" numbers or you are talking about theory in which something is "defined" as exactly zero - again, this would be a case of an integer. If you measure any quantity as zero, it is an approximation no matter how you look at it (again, excluding counts, which we know to be integers - and the case when we are talking about integers, N/0 is undefined as we all agree).

I realize the argument I am making is redundant as I've said it over and over again:

I know, you've been over this...bla...bla...bla.

But you still don't understand, so I feel compelled to explain again and again