Proof that (-a)(-b)=ab: Is It Logical?

[nickto21]

Hey All,
I found this proof on the internet, but its logic seems flawed.
Let x = (-a)(-b)
=(-1 * a)(-1 * b)
=-1 * a * -1 * b
=-1 * -1 * a * b
=(-1 * -1)(a * b)
= ab
So it's saying that (-a)(-b) = ab. This doesn't seem like a logical proof, or at least a satisfying one. Using what you're trying to prove in the proof itself seems wrong. It's trying to prove that two negatives multiplied together equal a positive, but it's using (-1 * -1) in the proof before it's been proven.
I'm trying to learn proofs, and this just seemed wrong, and I wanted clarification.
I appreciate any feedback.
Steve

 

[Hurkyl]

but it's using (-1 * -1) in the proof before it's been proven.

Read further back in whatever source you're using -- this was probably proven earlier. Specifically, it seems to have already proven/assumed that (-x) = (-1) * x, and I bet has also shown that -(-x)=x.

 

[nickto21]

Thanks for the reply. I"ll check on what you suggested.
BTW, Is there a software program that makes posting math symbols easier?
Maybe a graphics program where I can just post an image?
Thanks,
Steve

 

[HallsofIvy]

On this board you can use LaTex. Just surround your code with [ tex ] and [ /tex] or [ itex] and [ /itex] (without the spaces):
\int_{-\infty}^\infty} e^{-x^2}dx

Click on that to see the code. There is also a thread about LaTex on this board.

 

[nickto21]

Thanks for the info, both of you.
Steve