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Bar


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 x^_ (voiced "x-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

 x^_=1/nsum_(i=1)^nx_i

of a set {x_i}_(i=1)^n.

2. The complex conjugate

 z^_=x-iy

for z=x+iy.

3. The complement F^_ of a set F.

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 (|x|) (Bringhurst 1997, p. 271).


See also

Double Bar, Hat, Macron, Single Bar, Vinculum

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References

Bringhurst, R. The Elements of Typographic Style, 2nd ed. Point Roberts, WA: Hartley and Marks, p. 271, 1997.

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Bar

Cite this as:

Weisstein, Eric W. "Bar." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Bar.html

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