Triple bar

This article is about the symbol. For the horse jump, see Oxer.

The triple bar, ≡, is a symbol used in formal logic. It has the appearance of a "=" sign with a third line.

Logically, it has a similar meaning to the if and only if coupler ⇔. However, in some texts ⇔ is used as a symbol in logic formulas, while ≡ is for reasoning about those formulas (as in metalogic).

In addition, it has the completely separate meaning of modular congruence in number theory: we write $a \equiv b \pmod N$ if N divides a − b.

This symbol is also used when it appears in an equation which is a definition of its left-hand side, that is an equation which is not derived but instead defined. Relatedly, it is used to signify an "identity" – i.e. an equality that remains true regardless of the values of any variables that appear within.

It is also used for "identical equality" of functions; one writes $f \equiv g$ for two functions f, g if we have $f(x) = g(x)$ for all x.

In chemistry, the triple bar can be used to represent a triple bond between atoms. For example, HC≡CH is a common short-hand for acetylene.

The triple bar character in Unicode as codepoint U+2261 ≡ identical to (HTML: ≡ ≡). LaTeX \equiv corresponds to the triple bar.