Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    presumably you know that 0.0=0

    so that 0=0.0=(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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Simple proof, just using the axioms
  1. Simple Ab Alge proof (Replies: 6)