But isn't infinity large enough to change that ;)
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Mats
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infinity * zero is undefined as is 5/0. the limit of the latter is another story (inf).
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.
>> And since when did canceling in multiplication give zero?
1 = 0. See first post.
I think he thinks that:
Which of course is still wrong.Code:x * 0 = 1 * 0 = 0 = 0
- - - - -
0 x 0 1 0
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. :D
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)?
Reread what I said again. One goes to inf and one goes to 0. Not that both go to inf.