Overline - Math and Science

Math and Science

In mathematics, an overline is used primarily in two situations: either to indicate a line segment:

or repeating decimal value:

• 1⁄₇ = 0.142857 = 0.1428571428571428571...

Since it is not always possible to format the number so that the overline is over a certain digit, it is often placed to the left of the digits that repeat:

• 3.¯3 = 3.3 = 3.333333333333...
• 3.12¯34 = 3.123434343434...

The overline is also used to indicate a sample mean:

• is the average value of

In set theory and some electrical engineering contexts, negation operators can be written as an overline above the term or expression to be negated.

Common set theory notation:

Electrical engineering notation illustrating De Morgan's Laws with the saying, "break the line, change the sign":

in which implied multiplication, the times (cross) and the dot all mean logical AND, and the plus sign means logical OR.

In the repetition and negation usages, this notation is also referred to as a vinculum.

The overline notation can indicate a complex conjugate and analogous operations.

• if, then

In physics, an overline sometimes indicates a vector, although boldface and arrows are also commonly used:

In crystallography, an overline indicates an improper rotation or a negative number:

• is the Hermann–Mauguin notation for a threefold rotoinversion.
• is the direction with Miller indices, .