Why is the product of two negatives a positive? I understand why this —
-5 * 6
— should be -30. It’s because if you add -5 to itself 6 times, you come up with -30.
But, one must wonder, why is the inverse so odd? How do you “add” something to itself a negative number of times? These leads us to the odd situation of -5 * 6 making sense, but 6 * -5 seeming weird.
These leads me to wonder who decided that two negatives reverse polarity and become a positive. Multiplication is a shortcut for addition, right? “Two times three” is the same as “two plus two plus two,” just shorter.
But the “shortcut for addition” theory breaks down with negatives because you can’t add something to itself a negative number of times. So it feels like this one was arbitrary. Someone just decided, apparently, that multipltying two negatives makes a positive. I can’t find a logical truth to it.
Perhaps it just felt right.