I gather from other threads that infinity does not fit well into math. And it is for this reason alone that 1/infinity must = 0.

But let's think about infinity in terms of the physical world. If we do this infinity would be equal to the universe. And 1 (unit of physical world) would be equal to a quark.

So, 1/infinity in math is analogous to quark/universe in the physical world. Well a quark is something so 1/infinity must have a value greater than 0. That is, all the quarks make up the universe in the physical world so:

1/infinity + 1/infinity + 1/infinity .... = 1

What a load of BS. Infinity fits in perfectly well with mathematics.
Why is the universe equal to infinity, and why is a quark one unit. What about the leptons, don't they count.

Umm...no.

Math is the only place that infinity fits well. If you put any credit in to the big bang theory, then the universe can't be equal to infinity, because it would have a limit, an end, a set value. Infinity has no end. Its..its..inifinite!!

Maybe this then

1/0 = undefined
0/1 = 0

0/0 = undefined
0 *1 = 0
0 +1 = 1
...

infinity * infinity = infinity
Infinity + infity = infinity
infinity - infinity = infinity
infinity * 1= infinity

infinity/0 = undefined
0/infinity = 0

1/infinity = undefined ---> 1 != infinity * infinity

the limit of (1/X) as X approaches infinity = 0.

What about it?

If you go by the logic you just used, then 1/0 = infinity, which is undefined, but has certain algebraic properties.

Division is a process of subtract and test. When you divide by 0 the subtraction has no effect and the process will never end. (or the battery dies.)
The infinite part is not the number, it is the processing time.
X - 0 = X
Zero is not much of a number. It is mainly a position keeper. The opposite of zero is not infinity, it is anything not zero. This is why
X/0 is undefined.

bunk.

1/infinity + 1/infinity + 1/infinity = 1


all the infinitessimal small bits of the universe make up the whole

why is this wrong?

Hi yayacatfight,

First of all (regarding your first post in this thread), infinite fits perfect in math... Some people just don't want to acknowledge that. You just have to handle it properly, because "infinity" is a very abstract object (and because it is incredibly abstract, using "everyday" experience to do things with it are doomed to fail).

Your analogy with "infinity being the universe" is totally flawed. Infinity is not real, it is something humans thought up, the universe was there before humans were there to think about it.
If you want to say "quark/universe" then what you really need to know is the number of quarks in the universe. Let's say that this number is 10⁸⁰ (I just made that up, don't know if it is accurate). Then one quark, represented by the number "1" in your ideas divided by the total universe would be like 1 / 10⁸⁰. This is indeed not zero, and adding 1 / 10⁸⁰ up 10⁸⁰ times indeed equals one.

However, 10⁸⁰ is not infinity.

The reasoning remains true for any finite number you pick (take 10^800000000 for all I care). Mathematically let's denote that by N, which we assume to be large, and let N be the number of quarks in the universe. One quark is represented by 1, so the ratio quark/universe is given by 1 / N. To get the total universe we add up everything:
N * 1 / N = 1

Now let's take N going to infinity (this is a limit, if you are unfamiliar with the concept... learn that first, because it is absolutely necessary to understand "infinity"). It is true that:

lim[ N -> oo ] of N * 1 / N = 1

This statement expresses: "for every number you can think of, adding [number] times 1/[number] gives you back 1".

What you are saying by 1/infinity + ... 1 / infinity = 1 is not the above statement, what you want is:

( lim[ N -> oo] N ) * ( lim[ N -> oo ] 1 / N )

But this is not defined mathematically. You can only split the limit if both the series converge (and this is not the case).

So to be brief: you're math is flawed.

Oh BTW: 1 / infinity = 0, this is not "an infinitesimal bit", it is nothing, noppes, zip, zilch, nada, njet, rien :).

Bye!

Crisp

Oh BTW: 1 / infinity = 0, this is not "an infinitesimal bit", it is nothing, noppes, zip, zilch, nada, njet, rien

Interesting:

1 / infinity = 0
then
2/ infinity = 0
then
3 / infinity = 0
......
then
infinity/infinity=0
(or infinity/infinity=1,
or infinity/infinity=infinity)

Actually I think technically infinity/infinity = undefined, or at least that's what I've heard from math friends. Punch it into a graphing calculator and that's what you get too. I think that the reason it doesn't = 1 is because infinity isn't technically a number.

Arrgghhh, I hate math!!!! :D

Originally posted by Xenu
Actually I think technically infinity/infinity = undefined, or at least that's what I've heard from math friends. Punch it into a graphing calculator and that's what you get too. I think that the reason it doesn't = 1 is because infinity isn't technically a number.

Arrgghhh, I hate math!!!! :D

You're probably right.

What about it?
If you go by the logic you just used, then 1/0 = infinity, which is undefined, but has certain algebraic properties.

Is this in response to me? Cos I said->
" 1/0 = undefined
0/1 = 0

0/0 = undefined ". I don't see how you could reach that conclusion.

--> 1/infinity = undefined.
It is not 0, BECAUSE 1 IS NOT EQUAL TO 0*INFINITY.

the limit of (1/X) as X APPROACHES infinity = 0. Just the limit, it is never realized.

X/inifinity = undefined.

thanks crisp and others. i think i'm starting to get it.

It's easy to tell that infinity/infinity != 1. Or at last to tell that it would not be logical. Because infinity * infinity = infinity.
And if that is so. So if infinity/infinity = 1.
Then infinity * infinity / infinity = 1 too. If that was true, then infinity would equal to 1. And it sure does not. So I think that, who ever he or she was, was right when he or she said that infinity does not fit in maths.

Andreas

infinity/infinity is an indeterminate form.

consider this: 2 x infinity = infinity

infinity/infity =1

2 x (infinity/infinity) =1

2 = 1


get your head straight

Originally posted by On Radioactive Waves
infinity/infinity is an indeterminate form.

consider this: 2 x infinity = infinity

infinity/infity =1

2 x (infinity/infinity) =1

2 = 1


get your head straight Isn't that flawed?

okay, 2 * inf = inf.

inf/inf = 1 (your example, not mine)

you then only multiple ONE side by 2... you can't do that? right?

do i really need to explain this? sure, i didnt do this in the correct order, but the whole thing is flwaed. that was the point




2=(2/1) x (inf/inf) = (2 inf / inf ) = (inf/inf) = 1

2=1

it dosnt matter how correct i make the steps, inf/inf is indeterminate and therefore cant be used in a procees like this

Ready, here is a paradoxic in which infinity rears its ugly head.

Definition x=y

Mult b.s by x xx=yx

Subtract yy from b.s. xx-yy=yx-yy

factorise (x-y)(x+y)=y(x-y)

divide b.s. by (x-y) x+y=y

sub in x=y y+y=y

2y=y

2=1

What went wrong here?

what does that have to do with infinity?

that is the trick you use on algebra students....... any calulus student should know this one

So where does it go wrong then?

if x=y then x-y=0

you cant divide by zero, thats undefined (not infinity !!!)

now, where does infinity come into this?

Yes but by some of the ridiculous arguements below by some (not you), this would be equal to infinity, or worse, 1.

well theres always

(infinity)^0 = 1 heh heh

this damn issue comes up about once every other relativity thread around this place

It's not an issue, it's a misunderstanding or misinterpretation

"issue" in their minds ;) :m:


lol on hlreed Division is a process of subtract and test. When you divide by 0 the subtraction has no effect and the process will never end. (or the battery dies.)


okay, I'm really begining to think you ARE a robot

Infinity is not a number, so don't think that it follows the same rules that numbers do. Where it's easy to get confused is when Infinity takes on some properties of numbers, so people have a hard time distinguishing fact from fiction.

Infinity/Infinity = Indeterminate

**Without going into detail of why this is true, think of this question: What is the ratio of real numbers between 0-1 and 0-10? There are an infinite number of real numbers between 0-1, and likewise, there are an infinite number of real numbers between 0-10, so the ratio is Infinity/Infinity. However, everyone knows that there aren't an equal amount of numbers between 0-1 and 0-10, so logically, the ratio isn't 1:1. There are different "types" of infinity-countable, uncountable, etc., so it's impossible to say that one infinity is always the same as another.

Similar logic can be applied to these other indeterminate forms:

Infinity - Infinity = Indeterminate

0^Infinity = Indeterminiate

Infinity^0 = Indeterminate

1/Infinity + 1/Infinity + 1/Infinity .... ad infinitum = Indeterminate (if I'm not mistaken)

i started this thread with the comment that infinity does not fit well into math, i think that this discussion is confirming that.

i believe that the amount of real numbers in between 0-1 and 0-10 is equal.

exactly equal!

as close as 0.9999.... and 1 anyway and i have been told those are exactly equal.

crisp:

Your analogy with "infinity being the universe" is totally flawed. Infinity is not real, it is something humans thought up, the universe was there before humans were there to think about it.

infinity may be a human invention but so is math.

Math isn't actually "invented" by mankind. Math did allways excist, even before mankind. Or are you saying that before we "invented" maths, if you were to have one object here, and one object there, then they would not become a total of two objects. Though I agree that infinity may be a human invention, because we don't know whether or not there is anything that is ininate.

Andreas

Originally posted by ryans
Ready, here is a paradoxic in which infinity rears its ugly head.

Definition x=y

Mult b.s by x xx=yx

Subtract yy from b.s. xx-yy=yx-yy

factorise (x-y)(x+y)=y(x-y)

divide b.s. by (x-y) x+y=y

sub in x=y y+y=y

2y=y

2=1

What went wrong here?

Subtract yy from b.s. xx-yy=yx-yy
0 = 0

Although I didn't know it was possible to end up in the "wrong place" if you use the "rules" correctly.

AndersHermansson :


Subtract yy from b.s. xx-yy=yx-yy
0 = 0



There is nothing wrong with that! 0=0 , that is fine. The trouble dosnt show up until division by zero.


FlyingHellfish:




0^Infinity = Indeterminiate

are you sure?

I'm going to clean this mess up right now.

http://mathworld.wolfram.com/Indeterminate.html



There are seven indeterminate forms involving 0, 1, and :

http://mathworld.wolfram.com/iimg830.gif

If complex infinity is allowed as well, then six additional indeterminate forms result:
http://mathworld.wolfram.com/iimg832.gif

what is the problem with 1^inf ?

Because if the 1 in 1^infinity is either a bit higher or a bit lower than one, then you wind up with either infinity or 0, respectibly.

By the way, in math and in physics, you always work with the limit towards infinity, never with infinity itself.

Red Rover,

By the way, in math and in physics, you always work with the limit towards infinity, never with infinity itself.

ANS: That is because infinity is a mathematical proposition and has no standing in physical reality.

If as has been said early on the Universe were infinite then it could not be expanding. Infinite is infinite and nothing can be bigger. Therefore the universe is not infinite since it is expanding (at least we think it is).:D

Wrong wrong wrong

First of all, the number of numbers between 0-10 is greater than between 0-1 even though both are infinite. It's called cardinality, LOOK IT UP.

And Mac, just because something is infinite, doesn't mean it can't get bigger.

ryans,

Yes, of course mathematically inf +1 = Inf but it is considered a larger set but in terms of the general use and definition of infinity the universe cannot be infinite and expand. Simply put Inf1 may not equal Inf2 but yet by definition nothing is larger than infinity.

That is why it is limited to special mathematical applications and is never considered a physical reality.

Originally posted by ryans
Wrong wrong wrong

First of all, the number of numbers between 0-10 is greater than between 0-1 even though both are infinite. It's called cardinality, LOOK IT UP.

And Mac, just because something is infinite, doesn't mean it can't get bigger.

ouch. i can t let that slide. this is simply incorrect. the set of real numbers in [0,1] and in [0,10] have the same cardinality.

ok, i just read a little about cardinality, so using one to one mapping we can say there ARE ten times as many reals inbetween 0-10 than 0-1. since we know there are an infinite number of reals in between 0-1, there are 10(infinity) between 0-10.

so how many are reals are there between 0 and infinity?

infinity(infinity)?

using one to one mapping we could also prove that infinity + infinity = 2infinity

Originally posted by On Radioactive Waves
AndersHermansson :






There is nothing wrong with that! 0=0 , that is fine. The trouble dosnt show up until division by zero.


FlyingHellfish:



0^infinity = Indeterminate


are you sure?

Oops...no...I was thinking of 1^Infinity. I confused addition with multiplication.

Originally posted by FlyingHellfish
Oops...no...I was thinking of 1^Infinity. I confused addition with multiplication.

again, are you sure (1^infinity is indeterminate) ? ;)

Multiply 1 by itself as many times as you like, it still equals one, by definition, even after an infinite amount of multiplications, that's a fact.

exactly. I was wondering why this page http://mathworld.wolfram.com/Indeterminate.html includes 1^infinity in indeterminates list..! Redrover's argument in an earlier post indicates if 1 is not exactly 1, then 1^inf is indeterminate. i don't agree with that condition. 1 is exactly 1, no more or no less.

Infinity is just an inversion of 0. You can approach null but never reach it in continous systems, the same is true about the infinity. Therefore

0-infitity = 0

Originally posted by everneo
exactly. I was wondering why this page http://mathworld.wolfram.com/Indeterminate.html includes 1^infinity in indeterminates list..! Redrover's argument in an earlier post indicates if 1 is not exactly 1, then 1^inf is indeterminate. i don't agree with that condition. 1 is exactly 1, no more or no less.

everneo-

i will tell you why 1^infty is indeterminate. when you evaluate limits of exponentials like that, it is most convenient to take the logarithm first. if the logarithm is indeterminate/divergant/finite, then so is the original expression.

log 1^infty == infty log 1 == infty * 0 == infty/infty

which, as we already know, is indeterminate. thus, so is 1^infty.

we can understand that more intuitively as well, if you still don t believe it. consider an expression like (1+1/n)^n. as n goes to infty, this looks like 1^infty, and the limit is e.

but the expression (1+1/n^2)^n also looks like 1^infty, only the base goes to 1 faster than the exponent goes to infinity. this number approaches 1.

i can write down an expression that looks like 1^infty, but the limit is 0, infty, or any finite number you like. thus you see that 1^infty is indeterminate.

Originally posted by yayacatfight
ok, i just read a little about cardinality, so using one to one mapping we can say there ARE ten times as many reals inbetween 0-10 than 0-1. since we know there are an infinite number of reals in between 0-1, there are 10(infinity) between 0-10.

so how many are reals are there between 0 and infinity?

infinity(infinity)?

using one to one mapping we could also prove that infinity + infinity = 2infinity

there is a one to one mapping between [0,1] and [0,10]. so there are not "ten times as many numbers", as you say. there are exactly the same amount of numbers in those two sets: aleph_1. this may be less obvious, but there is also a one to one mapping between [0,1] and [0,infty], so there are exactly the same number of numbers in the unit interval as there are on the whole real line out to infinity. aleph_1.

if you think this is weird, well things get weird when you start dealing with the mathematics of infinity. you can t rely on your intuition too much. just because on line segment is 10 times as long as another, does not mean it has 10 times as many numbers. and an infinitely long line segment can have the same number of numbers as a finite line segment.

Man I sure admire you badass math mofos. Seriously, it's most impressive to me. Yay you guys!

Originally posted by wesmorris
Man I sure admire you badass math mofos. Seriously, it's most impressive to me. Yay you guys!

yeah, it sure is sweet being a math mofo. although it would be sweeter if it helped you get chicks.

(-:

Originally posted by lethe
yeah, it sure is sweet being a math mofo. although it would be sweeter if it helped you get chicks.

(-:
with your maths you can convert ducks into chicks, man. ((-;

thanks for the post, lethe.

now i'm really confused

i think i went full circle, i was beginning to understand why there were the same amount of numbers between 0 and 1 and 0 and 10 and then someone said learn cardinality. so i looked up some stuff and read about one to one mapping which made sense. and now we are back to them being exactly the same number.

is this subjective? or is it one or the other?

Originally posted by yayacatfight

is this subjective?
no

or is it one or the other?
yes. [0,1],[0,10] and [0,infty] all have the same "number of numbers" (cardinality). aleph_1.

thanks, got it.

Originally posted by yayacatfight
thanks, got it.

have you? well, can i give you an exercise?

construct a one to one mapping between [0,1] and [0,10]. if that s too easy, construct a one to one mapping between [0,1] and [0,infty], thus proving that they have the same cardinality.

no, i don't understand the cardinality part. it confused me. the one to one mapping is what made me think that there were 10 times as many numbers between 0-10 as 0-1.

but intuitively, prior to the mention of cardinality, as i have learned in another thread that in math 0.99999... = 1, it led me to think of a line segment between 0-1 and a line segment between 0-10. as you divide these line segments in half repeatedly the more times you do the closer the divisions become equal length to eachother. until they become equal to the ratio .9999999.... to 1.

not sure if that is correct but that's how it makes sense to me.

Originally posted by yayacatfight
no, i don't understand the cardinality part. it confused me. the one to one mapping is what made me think that there were 10 times as many numbers between 0-10 as 0-1.

but intuitively, prior to the mention of cardinality, as i have learned in another thread that in math 0.99999... = 1, it led me to think of a line segment between 0-1 and a line segment between 0-10. as you divide these line segments in half repeatedly the more times you do the closer the divisions become equal length to eachother. until they become equal to the ratio .9999999.... to 1.

not sure if that is correct but that's how it makes sense to me.

this doesn t seem like a good way to think about it to me: if you divide [0,1] and [0,10] into smaller and smaller pieces, say, by halving it each time, the pieces that you get from the [0,10] interval will always be 10 times as big.

hmmm, yep, i guess i was using line segment visually and when i did it that way they seemed to be getting closer in length but that is only in absolute terms.

i guess i should read some more about cardinality. back in a bit.

Originally posted by yayacatfight
hmmm, yep, i guess i was using line segment visually and when i did it that way they seemed to be getting closer in length but that is only in absolute terms.

i guess i should read some more about cardinality. back in a bit.

yeah, go read some more. that s always a good thing. if you want the answer, just ask. you ll kick yourself when you see how easy it is.

you'll have to tell me, i can't figure it out. i see that the integers are one set of infinity and the next infinity is any continuum of real numbers but i don't understand how you can map these so the reals between 0-1 and 0-10 are the same infinity.

i can see why georg cantor went insane

Originally posted by yayacatfight
you'll have to tell me, i can't figure it out. i see that the integers are one set of infinity and the next infinity is any continuum of real numbers but i don't understand how you can map these so the reals between 0-1 and 0-10 are the same infinity.

i can see why georg cantor went insane

OK. so to prove that [0,1] and [0,10] have the same number of numbers, you just have to find a mapping that takes all the numbers from the first bunch to the second bunch, it has to take each number from [0,1] to one and exactly one number in [0,10]. also it has to hit every number in [0,10]. a mapping that satisfies the first requirement is called one to one or an injection, and a mapping that satisfies the second condition is called onto or a surjection. a mapping that is both surjective and injective is called a bijection. by definition, two sets have the same cardinality if there exists a bijection between them. the task is to find such a mapping.

so here it is: 10x

if x is in [0,1] then 10x is in [0,10]. it is almost trivially obvious that 10x is both surjective onto the set [0,10] and injective. so the two sets have the same cardinality. QED.

it s slightly harder to think of a function that maps [0,1] to [0,infty] but it can be done too. lemme see...

1/x-1 should do the trick.

Lethe:

Cardinality....ugh! Sounds like set theory flashback to me. What again, did you say would happen if you woke up in a left hand universe?

What some of you guys are mixed up with all of this and your crackpot theories so... this is what I know from my High School Math:
1) infinity divided by infinity is not 1 or 0 its infinity because you do not know the number of infinity and I doubt you ever will.
2) from what I've been taught 1 divided by 0 isn't undefined in a limit and is equal to infinity and by the direction on the graph of the x function for example in 1/x as x approaches 0 decides if it is a negative or positive infinity which exists.

I dunno if these are entirely correct by is the best of my knowledge on this matter.

i think your all crack pots who have missed the point, infinity is a concept not a number, you cant add or subtract concepts, its an idea not a value, so dont use it as one

Originally posted by Kyleiskool
What some of you guys are mixed up with all of this and your crackpot theories so... this is what I know from my High School Math:
1) infinity divided by infinity is not 1 or 0 its infinity because you do not know the number of infinity and I doubt you ever will.
2) from what I've been taught 1 divided by 0 isn't undefined in a limit and is equal to infinity and by the direction on the graph of the x function for example in 1/x as x approaches 0 decides if it is a negative or positive infinity which exists.

I dunno if these are entirely correct by is the best of my knowledge on this matter.

No.

1)Infinity divided by infinty can be infinty or finite. It depends on the rate of increase in the numerator and the denominator.

2) The limit can be infinty, or it can be finite. take for example y=1 and then multiply by a special case of 1: (x-1)/(x-1)

f(x)= (x-1)/(x-1)

this function looks like f(x)=1 in all respects except at the point discontinuity at x=1 where the denominator is zero, and the limit is 1.

Is infinity a process or a state:

if infinity is a state then infinity/infinity = 1

Infinity is an approximation:

lim x-> infinity

x = infinity
2x = infinity

x/2x = infinity/infinity = 1/2

infity is used to represent approximately a very high number.

One of the problems here is that there are multiple concepts of infinity floating around in this thread. Sticking just to the mathematical ones for the moment: Cardinality works really well for sets, but doesn't really work well for some other applications. If you want to talk about ordered sets, then you really need to bring in ordinality. Infinity as the limit of a function can't be dealt with by either cardinality or ordinality. Du Bois_Reymond published some stuff on infinite limits back in the 19th century, but with the exception of a pamphlet by Hardy, I don't know of anyone who's run with it.

There are a lot of notions that really have little to do with mathematics. If you want to talk about "infinite being", you're probably not talking about anything to do with numbers and magnitude.

First get clear on what you mean by "infinity". What is the core notion you want to work with? What work do you want to do with it? Once you've done that, then we can take a look at how it fits in with math. Until then it's just adding on to the confusion as we switch from one concept to the next.

This is the math and physics section right? We'll just leave that philosophical infity for the philosophy forum.

Originally posted by On Radioactive Waves
This is the math and physics section right? We'll just leave that philosophical infity for the philosophy forum.

Sure, that's fine. Except that the divide between physics and metaphysic stretches thin when you start talking cosmology. But my point is that it hasn't been lift to the philosophy forum. It's all through this thread. Furthermore, even within this thread there seems to be confusion regarding the various mathematical notions of infinity. Until one can decide the subject of a conversation, it's very difficult to say anything definitive about it.

OK. so to prove that [0,1] and [0,10] have the same number of numbers, you just have to find a mapping that takes all the numbers from the first bunch to the second bunch, it has to take each number from [0,1] to one and exactly one number in [0,10]. also it has to hit every number in [0,10]. a mapping that satisfies the first requirement is called one to one or an injection, and a mapping that satisfies the second condition is called onto or a surjection. a mapping that is both surjective and injective is called a bijection. by definition, two sets have the same cardinality if there exists a bijection between them. the task is to find such a mapping.

so here it is: 10x


I don't get how 10x would hit every number in [0,10] satisfying the second condition. I can see it in reverse, but multiplying by 10 is skipping 9 numbers every time.

Originally posted by yayacatfight
satisfying the second condition. I can see it in reverse, but multiplying by 10 is skipping 9 numbers every time.

Look at 1/10 to go back. Divide each number in [0, 10] by 10 and you get a number in [0, 1]. Multiply each number in [0, 1] by 10 and you get a number in [0, 10]. Thus there is an bijective function between the two sets. Thus the sets have the same cardinality.

ok. so cardinality means the sets share the same general idea of infinity, not that they contain the exact same amount of numbers, is that right?

Originally posted by yayacatfight
ok. so cardinality means the sets share the same general idea of infinity, not that they contain the exact same amount of numbers, is that right?

Cardinality is one way of defining what you mean when you say "exact same amount".

Look. Suppose you didn't know how to count and I gave you two bags of marbles and asked you to tell me whether they had the same number of marbles in them. What would you do? One thing you could do would be to line the marbles up in two rows, pairing one marble from bag A with another from bag B. If the two bags run out of marbles at the same time, they have the same number of marbles. If one bag runs out before the other, it has fewer marbles.

WHen you count the marbles, you essentially do the same thing. You pair the marbles from bag A with the list of numbers you've memorized. Then you pair the marbles from bag B with the same list. If both bags of marbles run out at the same point, they have the same number of marbles in them.

Cardinality just extends this method to infinite sets. If you have two infinite sets and you want to compare how big they are, you just start pairing members from one set with members from the other. If it's possible to pair the members of the two sets without any remainder, i.e. if you can make it so that both sets run out at the same time, then the sets are the same size. If you can't do that, then they aren't.

The odd thing about infinite sets is that paring their members can give different results. Some pairings may exhaust both sets at the same time, while other pairing show one or the other set running out first. That's why the definition is given in terms of possibility. As long as there's some way of pairing that exhausts the sets simultaneously, then we say they are the same size. At least from the standpoint of cardinality.

Originally posted by thefountainhed
Maybe this then

1/0 = undefined
0/1 = 0

0/0 = undefined
0 *1 = 0
0 +1 = 1
...

infinity * infinity = infinity
Infinity + infity = infinity
infinity - infinity = infinity
infinity * 1= infinity

infinity/0 = undefined
0/infinity = 0

1/infinity = undefined ---> 1 != infinity * infinity

the limit of (1/X) as X approaches infinity = 0.

No, infinity - inifinity != infinity.

Sorry, you are wrong.

This is like saying lim(x->0) (1/x - 1/x) = oo

Work on your calculus, :)


James Sibley

Originally posted by 4DHyperCubix
No, infinity - inifinity != infinity.

Sorry, you are wrong.

This is like saying lim(x->0) (1/x - 1/x) = oo

Work on your calculus, :)


James Sibley

Actually it depends on what you mean by infinity.

If you have an infinite set and you remove an infinite number of members from it, you may still have an infinite number of members left it.

Consider the set of natural numbers. Now remove the set of even numbers from it. You are left with the set of odd numbers, which is infinite.

Originally posted by drnihili
Actually it depends on what you mean by infinity.

If you have an infinite set and you remove an infinite number of members from it, you may still have an infinite number of members left it.

Consider the set of natural numbers. Now remove the set of even numbers from it. You are left with the set of odd numbers, which is infinite.

I know what you mean. I read some stuff on Cantor and his work with infinity. I have not got very deep into it because I am only 18 right now and I got a lot of other things I am learning about math.

Well, if you take lim(x->0)(1/x^2 - 1/x) = y,
then y = oo... in this case, one could say infinity - infinity = infinity. However, we call this an indeterminate case, like 0*infinity and 1^infinity because you cannot assign a 'value' that will always work.

In case anyone is interested why 1^(oo) does not work, take this example:

e = lim(x->oo) (1 + 1/x)^x = 1^(oo) = 1.
Note how that is obviously incorrect.

Good day :)
James Sibley

1/infinity is a fraction, just like 1/2.

I can cut an apple in half.

I can walk half a mile.

Is 1/infinity the opposite of infinity?

<i>Is 1/infinity the opposite of infinity?</i>

Define "opposite".

Originally posted by Jerry
1/infinity is a fraction, just like 1/2.

I can cut an apple in half.

I can walk half a mile.

Is 1/infinity the opposite of infinity?

Can you count halfway to infinity?

Can you count halfway to infinity?

no.

But :

a = x (any number)

h= half of infinity

b = all numbers < a

c = all numbers > a

c=b

a=h

Ah, but see there's the problem. (same one I've been harping on in Zeno's paradox.) Defining infinity, or half of infinity inthis case, is not the same as counting to it.