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Simple proof, just using the axioms

  1. Jan 22, 2004 #1
    How could I show that (-m)(-n)= mn? The only thing I am allowed to use to prove this are the 5 basic mathematical axioms which allow for the commutative property and associative propery of the binary operations multiplication and addition;there exists an additive inverse for each integer, 1 is the multiplicative identity, and 0 is the additive identity, while mn=mp implies p=n where m is not equal to 0.
     
  2. jcsd
  3. Jan 22, 2004 #2

    matt grime

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    presumably you know that 0.0=0

    so that 0=0.0=(1-1)(1-1)=1-1.1+1.(-1)+(-1)(-1),

    =>

    1=(-1)(-1)

    the general case now follows easily from the fact -n = (-1).n

    you could do it more directly 0=m-m=n-n but you'd still have to use -n=(-1).n at some point.
     
  4. Jan 22, 2004 #3
    Thanks my man
     
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