1. Originally Posted by cpjust
Shouldn't those both equal 0? Anything times 0 equals 0 right?
But isn't infinity large enough to change that

--
Mats

2. infinity * zero is undefined as is 5/0. the limit of the latter is another story (inf).

3. Originally Posted by @nthony
infinity * zero is undefined as is 5/0. the limit of the latter is another story (inf).
Yeah, I remember my teachers always saying that x/0 is undefined, not infinity; but why is infinity * 0 undefined?

4. Originally Posted by cpjust
Yeah, I remember my teachers always saying that x/0 is undefined, not infinity; but why is infinity * 0 undefined?
Because infinity * 0 = infinity / (1/0) = infinity / infinity, which I think we already did.

5. Originally Posted by tabstop
Because infinity * 0 = infinity / (1/0) = infinity / infinity, which I think we already did.
Well using that logic: if x/0 = infinity and 0/x = 0 then

Code:
```x * 0  = 0
0   x```
because then the x's and 0's would cancel each other out and you'd be left with 0.

6. Originally Posted by cpjust
Yeah, I remember my teachers always saying that x/0 is undefined, not infinity; but why is infinity * 0 undefined?
Well to begin with infinity is not a number. You really can't multiply, divide, add, or subtract it. We can however talk about a function that goes to infinity given a certain condition.

inf * 0 is an indeterminate form as it depends on what f(x) and g(x) really are. Say f(x) goes to infinity twice as fast as g(x) goes to 0 you'll get a different result then if the situation was reversed.

7. Originally Posted by abachler
Well part of the problem comes from differeing definitions of infinity. In mathematical terms infinity is a fixed quantity that exists outside the set of real numbers. Most laymen think of it as a really large number'. Its not really large it is in fact unquantifiably large. It cannot be treated as so large that it simply obliterates all other values that are entangled with it, it must be treated as a unique quantity and kept serpate from the entangled terms, just as the imaginary number i must be treated as a seperate quantity, otherwise the maths break down.

5i * 5i yields 25i^2 = -25, not 25i

5 * infinity * 5 * infinity = 25 * infinity ^2, not 25 infinity or inifinty

5/0 = 5 * infinity not infinity

5/0 * 0 = 5

5*infinity * 0 = 5

If you do NOT treat infinity and hence division by zero as special unique quanities then the maths break down and in that illogical realm yes, you can prove any number to equal any other number, which is itself the proof that you must keep them seperate.
You have got it very, very wrong. You even state yourself that infinity must be treated uniquely, but then you continue to use it like a number anyway!

8. Originally Posted by cpjust
Well using that logic: if x/0 = infinity and 0/x = 0 then

Code:
```x * 0  = 0
0   x```
because then the x's and 0's would cancel each other out and you'd be left with 0.
And since when did canceling in multiplication give zero?

9. >> And since when did canceling in multiplication give zero?

1 = 0. See first post.

10. I think he thinks that:

Code:
```x * 0 = 1 * 0 = 0 = 0
-   -   -   -   -
0   x   0   1   0```
Which of course is still wrong.

11. Originally Posted by Thantos
I think he thinks that:

Code:
```x * 0 = 1 * 0 = 0 = 0
-   -   -   -   -
0   x   0   1   0```
Which of course is still wrong.
Well it's been a while since I've done that kind of math, but now that I think of it, yes that's what I meant.

But putting all the math stuff aside for a second - aren't 0 and infinity exact opposites?
I mean infinity is basically everything, whereas 0 is nothing. So combine them together and they annihilate each other like matter and antimatter.

12. Um no. If anything would be opposites it would be inf and -inf but even those are just concepts.

Just think about this for a bit: Suppose you had f(x) and g(x). One goes to infinity and the other goes to zero as x approaches some value. Now if f(x) is changing faster then g(x) wouldn't you expect to get a different answer then if the g(x) was changing faster then f(x)?

13. Originally Posted by Thantos
Um no. If anything would be opposites it would be inf and -inf but even those are just concepts.

Just think about this for a bit: Suppose you had f(x) and g(x). One goes to infinity and the other goes to zero as x approaches some value. Now if f(x) is changing faster then g(x) wouldn't you expect to get a different answer then if the g(x) was changing faster then f(x)?
Yes, 2(inf) will grow twice as fast as 1(inf), but they'll both keep going forever.

14. Reread what I said again. One goes to inf and one goes to 0. Not that both go to inf.

15. Originally Posted by Thantos
Reread what I said again. One goes to inf and one goes to 0. Not that both go to inf.
Oh, I see.
I'm still not sure what that has to do with my "inf * 0 = 0" comment though?