Why Does A Negative Times A Negative Equal A Positive?

The product of two negatives is a positive. Rules such as this one are chosen. For example, it is possible to chose the rule that the product of two negatives gives a negative. It is even possible to chose the rule that the product of two negatives is always 1792!

What is the general criteria for selecting which rules to adopt? Beauty, simplicity and utility are some considerations. Here is an argument for the product of two negatives giving a positive:

• Assume a < 0 and b < 0.
• a (b + (-b)) = 0 is desirable.
• Therefore, ab = - (a(-b)) is desirable.
• -(a(-b)) > 0
• Therefore, ab > 0 is also desirable.