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Weird question about dividing by zero

  1. Mar 3, 2012 #1
    Ok let a and b be non zero numbers

    ([itex]\frac{a}{b}[/itex]) / ([itex]\frac{1}{0}[/itex])=0

    But shouldn't that be undefined since you would get a fraction like this [itex]\frac{1}{0}[/itex] which isn't allowed. Since it got us to a "wrong" answer, that would mean our assumption was wrong. Please tell me where I went wrong.


    Not homework just got thinking about how 1/0 is undefined while 0/1 isn't

    (I typed everything wrong please look below)
     
    Last edited: Mar 3, 2012
  2. jcsd
  3. Mar 3, 2012 #2

    Office_Shredder

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    0/1 is just 0. It's when you divided by 0/1 (and hence divided by 0) that you get trouble. Why do you think the fraction you wrote down is equal to zero?
     
  4. Mar 3, 2012 #3
    I checked it on my calculator (or at least i thought I did) and it said 0. I did the inverse calculation (1/0) which I think makes more sense now.

    Why is it that when I divide x by 1/0 I get 0 instead of an undefined answer

    http://www.wolframalpha.com/input/?i=(a/b)/(1/0)

    So please ignore my error in typing. I'm going to go edit it.
     
  5. Mar 3, 2012 #4

    Office_Shredder

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    It could be wolfram alpha is too smart for its own good
    [tex] \frac{a/b}{1/0} = \frac{a}{b} \frac{0}{1} = 0[/tex]

    Of course writing 1/(1/0) = 0/1 doesn't make any sense, but you can easily imagine a computer program not caring about that when it simplifies fractions.

    However that's not the case here specifically

    http://www.wolframalpha.com/input/?i=1/0

    1/0 is defined by wolfram alpha as complex infinity (in the complex plane, all the infinities are actually the same, as opposed to in the real case where it's natural to talk about positive and negative infinity). So basically you're asking for (a/b)/infinity and of course when you divide by infinity you get zero.

    I think it's a poor job by wolfram alpha to define 1/0 as infinity like that to be honest, but it's probably done for added flexibility in performing other calculations
     
  6. Mar 3, 2012 #5
    I agree with everything you said. But shouldn't we stop and say 1/0 is impossible. Stop the presses!

    I checked on other calculators as well. like a google search and my personal calculator. It must be a computation thing.
     
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