# A proof

1. Sep 19, 2010

### Jimmy84

1. The problem statement, all variables and given/known data
prove that if a is less than zero , and if b is less than zero then ab is greater than zero.

I have been having troubles with this problem.
thanks.

2. Relevant equations

3. The attempt at a solution

2. Sep 19, 2010

### Office_Shredder

Staff Emeritus
What have you tried so far? Do you know what axioms for positivity you can use?

3. Sep 19, 2010

### Jimmy84

Im reading the subject in the book of Spivak and frankly I dont understand what he says.
on page 12 he defined P to be a positive number thenhe said that for a number a only one of this three equalities is correct

a=0, a is a is part of P, and - a is part of P. I dont understand the last one since he defined P as the set of all the positive numbers maybe there might be a mistake in my book though.

is there any other way to prove this theorem?

4. Sep 19, 2010

### Office_Shredder

Staff Emeritus
For example, if a=-3, then -a is in P, not a.

You're going to have to use his definition of positivity to do the problem. You can't prove that something has a certain property without using its defining features!

As a starting point: We know that a<0 and b<0 here, so (-a)>0 and (-b)>0. Try to work from here