# Minus signs are ambiguous

The minus sign has two common usages:

• A single value prefixed with a minus sign indicates a negative, e.g. $-5$ means the same as $\overline{5}$. (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. $5-2$ 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. $2x$ to mean “$2$ times $x$”. Using the minus sign for two different operations makes this ambiguous, since $2-x$ could mean “two times negative $x$or it could mean “two take away $x$”; 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. $2\left(-x\right)$

## 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.