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Little doubt: elementary math

  1. Apr 20, 2006 #1
    i'm a hight school student and this is a stupid question:

    why "3 x 0 = 0" and "3/0 = nothing"? should make 0 too.

    it bothers me from years
  2. jcsd
  3. Apr 20, 2006 #2


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    Homework Helper

    "3/0" is not 'nothing', it is left 'undefined'. Why should it be zero?
  4. Apr 20, 2006 #3


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    division by zero is undefined.

    Division is defined as multiplying by the inverse. Say you write a/b = x, you actually mean a * b^(-1) = x, where b^(-1) is defined the be the unique number such that b * b^(-1) = 1 = b^(-1) * b.

    However, 0^(-1) does not exist: suppose it did. Then, 0 * 0^(-1) = 1. But for any a, 0 * a = 0. Hence, we have an obvious contradiction.

    Thus, saying a/0 = a * 0^(-1) = x is completely meaningless, since 0^(-1) does not exist.
  5. Apr 21, 2006 #4
    you can't divide 3 staws into zero groups.
    You could divide them into 1 group of 3, or 3 groups of 1, or others if you cut the straws into smaller pieces. No mater how small the pieces there will just be more and more groups.
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