And while we're at it, I think that when we teach arithmetic, we should be representing negative numbers using compliments like computers do. It makes negation a little more difficult, but still pretty easy, and eliminates subtraction as a distinct concept from negation and addition, along with the entire subtraction table.

So, for example, a -2 is like saying . We're used to having a weird unnecessary special case when going below zero, but if we mechanically use the normal subtraction rules, realizing that there are an infinite number of implicit leading zeros for these numbers, we see it's really a case of $¯ ¯ ¯ 0 0 - 2$ . Normally when subtracting digit-by-digit, you borrow one from the next digit, e.g. $100 - 002$ becomes $108 - 010$ then $198 - 100$ , then $098 - 000$ or just 98. So for $¯ ¯ ¯ 0 0 - 2$ the borrowing continues indefinitely and it becomes $¯ ¯ ¯ 9 8$ . Add two to this and it flips all the nines, so we're back to zero. You can represent any negative number this way and then "subtraction" is just normal addition.