# Triple bar

≡ | |
---|---|

Identical to | |

U+2261 ≡ IDENTICAL TO (≡, ≡) |

≢ | |
---|---|

Not identical to | |

U+2262 ≢ NOT IDENTICAL TO (≢, ≢) |

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 as output.^{[2]}

## Uses

### Mathematics and philosophy

In

^{[5]}Gottlob Frege used a triple bar for a more philosophical notion of identity, in which two statements (not necessarily in mathematics or formal logic) are identical if they can be freely substituted for each other without change of meaning.

^{[6]}

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: 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

^{[13]}

^{}[14] Similarly, another alternative notation for this usage is to precede the equals sign with a colon, . The colon notation has the advantage that it reflects the inherent asymmetry in the definition of one object from already defined objects.

### Science

In

^{[15]}

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