Vinculum (symbol)

{\overline {\rm {AB}}}

line segment from A to B

1⁄7 = 0.142857

repeated 0.1428571428571428571...

{\overline {a+bi}}

complex conjugate

Y={\overline {\rm {AB}}}

boolean NOT (A AND B)

{\sqrt[{n}]{ab+2}}

radical ab + 2

a-{\overline {b+c}}

= a − (b + c)

bracketing function

Vinculum usage

A vinculum (from Latin vinculum 'fetter, chain, tie') is a horizontal line used in mathematical notation for various purposes. It may be placed as an overline or underline above or below a mathematical expression to group the expression elements. Historically, vincula were extensively used to group items together, especially in written mathematics, but in modern mathematics its use for this purpose has almost entirely been replaced by the use of parentheses.^[1] It was also used to mark Roman numerals whose values are multiplied by 1,000.^[2] Today, however, the common usage of a vinculum to indicate the repetend of a repeating decimal^[3]^[4] is a significant exception and reflects the original usage.

^ Cajori, Florian (2012) [1928]. A History of Mathematical Notations. Vol. I. Dover. p. 384. ISBN 978-0-486-67766-8.
^ Ifrah, Georges (2000). The Universal History of Numbers: From Prehistory to the Invention of the Computer. Translated by David Bellos, E. F. Harding, Sophie MENGNIU, Ian Monk. John Wiley & Sons.
^ Childs, Lindsay N. (2009). A Concrete Introduction to Higher Algebra (3rd ed.). Springer. pp. 183-188.
^ Conférence Intercantonale de l'Instruction Publique de la Suisse Romande et du Tessin (2011). Aide-mémoire. Mathématiques 9-10-11. LEP. pp. 20–21.

[1] Cajori, Florian (2012) [1928]. A History of Mathematical Notations. Vol. I. Dover. p. 384. ISBN 978-0-486-67766-8.

[2] Ifrah, Georges (2000). The Universal History of Numbers: From Prehistory to the Invention of the Computer. Translated by David Bellos, E. F. Harding, Sophie MENGNIU, Ian Monk. John Wiley & Sons.

[3] Childs, Lindsay N. (2009). A Concrete Introduction to Higher Algebra (3rd ed.). Springer. pp. 183-188.

[4] Conférence Intercantonale de l'Instruction Publique de la Suisse Romande et du Tessin (2011). Aide-mémoire. Mathématiques 9-10-11. LEP. pp. 20–21.

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