Triple bar.html

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.

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.

It is Unicode character 8801. The HTML entity &equiv; also corresponds to the triple bar.

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