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Giving infinity a value

  1. Aug 24, 2015 #1
    Is infinity divided by infinity equal to 1? 6 divided by 6 is equal to 1 however as infinity resembles 0 in the sense that 0 dived by 0 is equal to 0, I am uncertain whether infinity divided by infinity would equal 1 or instead, infinity.
     
  2. jcsd
  3. Aug 24, 2015 #2

    DEvens

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    Education Advisor
    Gold Member

    Usually you can't do things like multiply or divide by infinity. It is not defined. Similarly, 0 divided by 0 is not 0. It is not defined.

    What you can sometimes do is examine a limit. So ##\lim_{x->0} \frac{\sin(x)}{x}## is defined, and is 1. So in this sense, in this case, dividing a zero by a zero gives you 1. But only as the limit.

    https://en.wikipedia.org/wiki/L'Hôpital's_rule
     
  4. Aug 24, 2015 #3
    The uncertainties of the type ##\infty \cdot 0##, ##\infty/\infty## or ##0/0## acquire a definite value only as a limit, you can't simply operate with ##\infty## as being a number. So, unless we can go through the limit process it makes no sense to say that some uncertainty is equal to some value.
     
  5. Aug 24, 2015 #4
    You are considering infinity as a constant number
    Depends on the infinities you are working with quotient of two infinities can be zero or infinity too
     
  6. Aug 24, 2015 #5
    Cheers for all your help
     
  7. Aug 31, 2015 #6

    Mark44

    Staff: Mentor

    You have managed to pack a number of things that aren't true into a small number of words.

    No.
    The indeterminate form ##[\frac{\infty}{\infty}]## shows up in calculus as limits that can literally come out to any number, as well as negative or positive infinity. Here are some simple examples:
    1. ##\lim_{x \to \infty}\frac{x^2}{x} = \infty##
    2. ##\lim_{x \to \infty}\frac{x}{x^3} = 0##
    3. ##\lim_{x \to \infty}\frac{x^2 + 3}{3x^2 - x + 7} = \frac 1 3##

    No, not at all.

    No.
    Division by 0 is not defined. The indeterminate form ##[\frac 0 0]## also shows up in calculus limits, and can come out to any number. Some examples of this:
    1. ##\lim_{x \to 0}\frac{x^2}{x} = 0##
    2. ##\lim_{x \to 0}\frac{x}{x^2}## does not exist
    3. ##\lim_{x \to 0}\frac{x}{x^3} = \infty##
    4. ##\lim_{x \to 0}\frac{\sin(2x)}{x} = 2##
     
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