Minus signs are ambiguous

Part of my units pages

The minus sign has two common usages:

This is a reasonable distinction on its own, but causes problems when expressions involve multiple values and operations. This makes things harder to learn, harder to teach, harder to program into a computer, etc.

For example, it’s common to write multiplication by putting values side-by-side, e.g. 2⁢xtimes2x to mean “22 times xx”. Using the minus sign for two different operations makes this ambiguous, since 2−x 2x could mean “two times negative xx” or it could mean “two take away xx”; these are two very different things! Convention is to always treat such minus signs as subtraction, and use parentheses if we want multiplication, e.g. 2 ⁢ ( -x )

Avoid unary minus: prefer over-bars for negatives

Compared to minus signs, “over-bar” notation seems to be more elegant for indicating negatives/opposites/inverses. It also extends naturally to the idea of negative digits.

Avoid binary minus: add negatives instead of subtracting

Addition is more “well behaved” than subtraction (it is commutative, associative, etc.), so it’s generally better to add negatives instead of subtracting.