A bar (also called an overbar) is a horizontal line written above a mathematical symbol to give it some special meaning. If the bar is placed over a single symbol,
as in 
(voiced "
-bar"), it is sometimes called a macron.
If placed over multiple symbols (especially in the context of a radical),
it is known as a vinculum. Common uses of the bar symbol
include the following.
1. The mean
 |
of a set 
.
2. The complex conjugate
 |
for 
.
3. The complement 
of a set 
.
4. A set stripped of any structure besides order, hence the order type of the set.
In conventional typography, "bar" refers to a vertical (instead a horizontal) single bar such as those used to denote absolute
value (
) (Bringhurst 1997, p. 271).
