Vinculum

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A vinculum is a horizontal line placed over a mathematical expression, used to indicate that it is to be considered a group. Vinculum is Latin for "chain", reflecting the function of the symbol.

Examples of its use include the case of a group of infinitely repeating digits, for example,

<math>\frac{1}{3} = 0.333333\dots = 0.\overline{3}</math>

It is also used in common arithmetic to denote that the numerator is being divided by the denominator as a whole group.

<math>\frac{500}{10*10} = \frac{5}{1} = 5</math>

It is also used in the notation of a radical to indicate the radicand whose root is being indicated. In the next case, the quantity <math>ab+2</math> is the radicand, and thus has a vinculum over it.

<math>\sqrt[n]{ab+2}</math>

The vinculum is also sometimes used in Boolean algebra, where it serves to indicate a group of expressions whose logical result is to be negated, as in

<math>\overline{AB}</math>

The vinculum should not be confused with a similar-looking vector notation, e.g. <math>\overrightarrow{AB}</math> "vector from A to B", or <math>\vec{a}</math> "vector named a".