Originally Posted by

**IAlexN**
Is there anyway to mathematically prove that any number; say X times Y equals a positive number Z.

Where X < 0, Y < 0 and Z > 0.

This is not homework. I'm just curious, since all my teachers have told me that any negative number times a negative number equals a positive number. Though, they never explained why.

Thank You!

Let x be a real number such that x < 0 and let y be a real number such that y < 0, where the following relationship holds true:

, for all z such that z > 0.

for all real numbers such that x < 0, y < 0, and z > 0.

QED

Now, in the above proof, we don't originally use the expression

, but

, look at what this does to the set that x and y belong:

As you can see from the above, using the negative coefficient of -1 for both numbers makes both of them positive, and we know that two positive numbers multiplied are positive, and we proved that an expression where both numbers had negative coefficients was equal to an expression where both numbers had the positive coefficient of one.