# 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.

## 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.