Why Does Multiplying Two Negative Numbers Yield a Positive?

[Jimmy84]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

 

[Office_Shredder]

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

 

[Jimmy84]

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

Im reading the subject in the book of Spivak and frankly I don't 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 don't 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?

 

[Office_Shredder]

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