Division Result

This is a discussion on Division Result within the Tech Board forums, part of the Community Boards category; What would be the result of the following divisions? Code: a. 1/0 b. 1/INFINITY c. INFINITY/0 d. 0/INFINITY e. INFINITY/1 ...

  1. #1
    Anirban Ghosh
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    Division Result

    What would be the result of the following divisions?

    Code:
    a. 1/0
    b. 1/INFINITY
    c. INFINITY/0
    d. 0/INFINITY
    e. INFINITY/1
    f. INFINITY/INFINITY
    g. 0/0

  2. #2
    a_capitalist_story
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    Negative infinity - 42. Obviously.

  3. #3
    and the Hat of Guessing tabstop's Avatar
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    Code:
    #include <stdio.h>
    #include <math.h>
    int main(void) {
        float a = 1.0f;
        float b = 0.0f;
        float c = INFINITY;
        printf("%f %f %f %f %f %f %f\n", a/b, a/c, c/b, b/c, c/a, c/c, b/b);
        return 0;
    }
    C99 at least is guaranteed to follow IEEE guidelines.

  4. #4
    C++ Witch laserlight's Avatar
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    Are you asking with respect to the rules of some branch of mathematics or a programming language?
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  5. #5
    The Right Honourable psychopath's Avatar
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    a. undefined
    b. nearly zero
    c. undefined
    d. zero
    e. infinity
    f. 1
    g.undefined (I think)
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  6. #6
    and the Hat of Guessing tabstop's Avatar
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    Quote Originally Posted by psychopath View Post
    a. undefined
    b. nearly zero
    c. undefined
    d. zero
    e. infinity
    f. 1
    g.undefined (I think)
    I'll give you 3.5/7 for that (at least as far as real analysis goes).

  7. #7
    & the hat of GPL slaying Thantos's Avatar
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    Trying to remember from calc 2 (it has been awhile and was probably the least useful semester) but isn't the division by inf indeterminate? IIRC you can talk about a variable as it approaches infinity but you can't use infinity as a number.

  8. #8
    Kernel hacker
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    Quote Originally Posted by laserlight View Post
    Are you asking with respect to the rules of some branch of mathematics or a programming language?
    This would be a critical question to get an answer to, as there is sometimes a significant difference between theoretical math and how a computer performs under those circumstances. Although I'm sure that both normally treat x/0 as "division by zero", where this normally leads to a hardware exception in a computer [so it stops the application] (but this is also usually configurable).

    As so often is the case, the question is not clear enough in it's scope to give a complete answer.

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  9. #9
    The Right Honourable psychopath's Avatar
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    Quote Originally Posted by Thantos
    IIRC you can talk about a variable as it approaches infinity but you can't use infinity as a number.
    In B I believe you would have to say that limit is zero as infinity is approached. But in D I was under the impression that whether you can treat infinity as a number or not, zero divided by anything had to be zero. And in F, anything divided by itself was always one.

    I could be completely wrong though. Only one year of precalc under my belt .
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  10. #10
    and the Hat of Guessing tabstop's Avatar
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    Well, for f, consider (x^2)/x. Both go to infinity as x gets large, but the quotient is still infinity. (And of course, you can go the other way to get a quotient of zero, which is why f is undefined.)

  11. #11
    & the hat of GPL slaying Thantos's Avatar
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    I don't think f is undefined but is indeterminate. I gotta dig out the book I think

  12. #12
    & the hat of GPL slaying Thantos's Avatar
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    And really since all but two are talking about infinity I have to assume that really means that as the function approaches some value it goes towards infinity. With the 0 it really depends if you mean:

    x / 0
    or
    x/f(y) as y approaches some number that causes f(y) to approach 0.

  13. #13
    and the Hat of Guessing tabstop's Avatar
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    Quote Originally Posted by Thantos View Post
    I don't think f is undefined but is indeterminate. I gotta dig out the book I think
    Same thing (or at least I meant by undefined what you mean by indeterminate).

  14. #14
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    I always thought that infinity is not a number, but a process, so an expression like 1/infinity is invalid and meaningless. You can express it as a limit, however, as in "(lim x->inf) 1/x". In that case, it's asking what value does 1/x approach as x approaches infinity. The answer would be 0.

    Anything divided by zero is undefined. "(lim x->0+) 1/x", though, is +inf, whereas "(lim x->0-) 1/x", is -inf.

    I have only taken one calculus course, though (AP calculus. graduating highschool this year ), so correct me if I'm wrong.

  15. #15
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    Quote Originally Posted by cyberfish View Post
    Anything divided by zero is undefined. "(lim x->0+) 1/x", though, is +inf, whereas "(lim x->0-) 1/x", is -inf.
    You can't have your cake and eat it too. What you say is not true when limits come into the picture. For example, the limit as x->0 of (x/x) is 1. Many basic results of differential calculus are based on such limits being defined.

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