Thread: 1=0.

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?

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.

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.

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.

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?

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

1 = 0. See first post.

I think he thinks that:

Code:

x * 0 = 1 * 0 = 0 = 0
-   -   -   -   -
0   x   0   1   0

Which of course is still wrong.

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.

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)?

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.

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

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?