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Is this True for all no.s?

  1. Aug 21, 2009 #1
    Is this True for all no.s??

    Is this true for all no.s (a)?
    a-a = a*0
  2. jcsd
  3. Aug 21, 2009 #2
    Re: Is this True for all no.s??

    In any number system that has additive and multiplicative identities, additive inverses, and is distributive, yes.

    [tex]a \cdot 0 = a \cdot (0+0) = (a \cdot 0) + (a \cdot 0)[/tex]

    This can only be true if [itex]a \cdot 0 = 0[/itex]

    [tex]a - a = a + (-a) = 0 \text{ by defintion.}[/tex]

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