Overline

Overline

[oh-ver-lahyn]
An overline or overbar (coined in analogy to underline, attested for mathematical notation since 1899), refers to the typographical feature of a line drawn immediately above the text, for example used to indicate medieval sigla.

In Unicode, there is U+0305 "combining overline" ̅ (the difference to a macron (U+0304) being that its cumulation results in an unbroken line, compare ̅̅̅ to ̄ ̄ ̄). ISO/IEC 8859-1 0xaf/Unicode U+00AF ¯ is called both "overbar" and "macron" and usually does not result in an unbroken line. In Codepage 850 distributed with MS-DOS, the overline is in position 238. Depending on the context it is used in, the overbar has different meanings.

Marking one or more words with a continuous line above the characters is also described as "overstriking".

The symbol should not be confused with other Unicode characters with the same name, even if they are also described as "macron". The character at codes U+02C9 (modifier letter macron) and U+0304 (combining macron) are clearly shorter than their counterparts named overline. The symbol described as combining merges with the preceding letters (for example: 0,1̅), compared with the code U+00AF (overline), which always functions as an independent symbol (for example: 0, 1¯).

In mathematics, an overline is used primarily in two situations: either to indicate a line segment (such as segment AB) or a repeating decimal value (such as 0.428571) which means 0.428571428571428571... (note the decimalization of three divided by seven repeats this way forever). Since it is not always possible to format the number so that the overline is over a certain digit, it is often used like: 3.¯3 for 3.333333333333... or 3.12¯34 for 3.123434343434... (That is, the digits to the right of the overline are periodically repeated.) The overline shows that the repeating part of the number is to its right.

The overline is also used in electronics documents and when indicating a statistical mean (for example, bar x)

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

Common set theory notation:

overline{A cap B}=overline{A} cup overline{B} iff overline{A cup
B}=overline{A} cap overline{B}

Electrical engineering notation illustrating the saying, "break the line, change the sign":

overline{A + B}=overline{A} times overline{B} iff overline{A cdot B}=overline{A} + overline{B} iff overline{AB}=overline{A} + overline{B} iff overline{A + B}=overline{A} cdot overline{B}
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

Producing in text software

  • In HTML using CSS, text, results in: text
  • In HTML documents, the characters can be produced with ¯ (decimal ¯) and ̅ (̅).
  • In TeX, a single symbol can be overlined with bar x or bar{x}. Longer sections can be overlined with overline{ABC}, where a space is written as " " and an umlaut is written as "ddot a".
  • In Microsoft Windows, the symbol can be added with any program with the keystrokes Alt+0175.
  • In Linux, the symbol can be added using the keystrokes Ctrl+Shift+U to activate unicode input, then type "00AF" as the unicode for the character.

Overstriking of longer sections of text, such as in 123 can also be produced in many text processors as text markup as a special form of understriking.

See also

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