Triple bar

The triple bar or tribar, ≡, is a symbol with multiple, context-dependent meanings indicating equivalence of two different things. Its main uses are in mathematics and logic. It has the appearance of an equals sign ⟨=⟩ with a third line.

Encoding

The triple bar character in Unicode is code point U+2261 ≡ IDENTICAL TO (≡, ≡).^[1] The closely related code point U+2262 ≢ NOT IDENTICAL TO (≢, ≢) is the same symbol with a slash through it, indicating the negation of its mathematical meaning.^[1]

In LaTeX mathematical formulas, the code \equiv produces the triple bar symbol and \not\equiv produces the negated triple bar symbol ${\displaystyle \not \equiv }$ as output.^[2]

Uses

Mathematics and philosophy

In

In mathematics, the triple bar is sometimes used as a symbol of identity or an equivalence relation (although not the only one; other common choices include ~ and ≈).^[7][8] Particularly, in geometry, it may be used either to show that two figures are congruent or that they are identical.^[9] In number theory, it has been used beginning with Carl Friedrich Gauss (who first used it with this meaning in 1801) to mean modular congruence: ${\displaystyle a\equiv b{\pmod {N}}}$ if N divides a − b.^[10][11]

In category theory, triple bars may be used to connect objects in a commutative diagram, indicating that they are actually the same object rather than being connected by an arrow of the category.^[12]

This symbol is also sometimes used in place of an equal sign for equations that define the symbol on the

An alternative notation for this usage is to typeset the letters "def" above an ordinary equality sign, ${\displaystyle a\mathrel {\stackrel {\scriptscriptstyle \mathrm {def} }{=}} b}$.

${\displaystyle a:=b}$

Science

In

In chemistry, the triple bar can be used to represent a triple bond between atoms. For example, HC≡CH is a common shorthand for acetylene^[16] (systematic name: ethyne).

Application design

See also:

justified text alignment. It is an oft-used component of Google's Material Design guidelines and many Android

apps and web apps that follow these guidelines make use of the hamburger menu.

References

Look up triple bar in Wiktionary, the free dictionary.

1. ^
   ISBN 978-0-19-957002-7
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2. ^ Lamport, Leslie (1994), LaTeX: A Document Preparation System (2nd ed.), Addison-Wesley, p. 43.
3. ISBN 978-0-87220-450-8
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4. ISBN 978-1-285-96556-7
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5. ISBN 978-1-84265-256-5
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6. ISBN 978-0-8126-9752-0
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7. ISBN 978-0-547-16509-7
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8. ^ Lambek, J.; Scott, P.J. (1986), Introduction to higher order categorical logic, Cambridge University Press, p. ix, Remark on notation: throughout this book, we frequently, though not exclusively, use the symbol ≡ for definitional equality.
9. ISBN 978-0-486-16116-7
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10. ISBN 978-3-540-34720-0
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11. ^ Cajori (2013), p. 34.
12. ISBN 978-0-493-91365-0
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13. ^ Meigs, John; Olmsted, Hubbell (1956), Intermediate analysis: an introduction to the theory of functions of one real variable, Appleton-Century-Crofts, p. vi.
14. ^ Lamport (1994), p. 50.
15. ^ "Guidelines for authors" (PDF), Taxon, 62 (1): 211–214, 2013
16. ISBN 978-0-8151-8450-8
17. ISBN 978-1-4493-6369-7
    .
18. ^ Cox, Norm, "The origin of the hamburger icon", Evernote