1=0.

This is a discussion on 1=0. within the A Brief History of Cprogramming.com forums, part of the Community Boards category; Originally Posted by cpjust Shouldn't those both equal 0? Anything times 0 equals 0 right? But isn't infinity large enough ...

  1. #46
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    Quote Originally Posted by cpjust View Post
    Shouldn't those both equal 0? Anything times 0 equals 0 right?
    But isn't infinity large enough to change that

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

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    Quote Originally Posted by @nthony View Post
    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?

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    Quote Originally Posted by cpjust View Post
    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.

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    Quote Originally Posted by tabstop View Post
    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.

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    Quote Originally Posted by cpjust View Post
    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.

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    Quote Originally Posted by abachler View Post
    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!
    Last edited by Sang-drax : Tomorrow at 02:21 AM. Reason: Time travelling

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    Quote Originally Posted by cpjust View Post
    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?

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

    1 = 0. See first post.

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    I think he thinks that:

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

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    Quote Originally Posted by Thantos View Post
    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.

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    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)?

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    Quote Originally Posted by Thantos View Post
    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.

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

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    Quote Originally Posted by Thantos View Post
    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?

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