Minus signs are ambiguous
The minus sign has two common usages:
- A single value prefixed with a minus sign indicates a negative, e.g. means the same as . (This is sometimes called “unary minus”, since it applies to a single value)
- A pair of values separated by a minus sign indicates subtraction, e.g. means “five take away two”. (This is sometimes called “binary minus”)
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. to mean “ times ”. Using the minus sign for two different operations makes this ambiguous, since could mean “two times negative ” or it could mean “two take away ”; 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.
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.