Simple proof, just using the axioms

[Ed Quanta]

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.

 

[matt grime]

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.

 

[Ed Quanta]

Thanks my man