Using $\pm$ to express "in the range of" statement.

Question

Does it make sense to write:

$x = \left\{A\pm B\right\}$

To mean that $x$ falls in the range of $\left\{A-B,A+B\right\}$?

If not, what would be the correct way of expressing this?

Many thanks!

Answer 1

The problem with $\pm$ is that it only refers to two points, not the range between them. Although $x = \{A \pm B \}$ is not commonly seem, I would take it mean that $x$ is $A+B$ or $A-B$.

One popular abuse of $\pm$ is when it's used to mean "approximately". Someone might say that something will happen in "plus or minus three days", and while that precisely means that it will happen three days in the future or it already happened three days in the past, but what they mean is "about three days".

To avoid confusion, the best time to use $\pm$ is when you have two possible answers depending on whether a term is positive or negative, like in the quadratic formula.