The triple bar, ≡, is a symbol with multiple, context-dependent meanings. It has the appearance of a "=" sign with a third line.
In logic, it has a similar meaning to the if and only if connective, ⇔. However, in some texts ⇔ is used as a symbol in logic formulas, while ≡ is for reasoning about those formulas (as in metalogic).
In mathematics it sometimes used a symbol for congruence (although not the only one). Particularly, in number theory, it has the meaning of modular congruence: 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 for two functions f, g if we have 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.
|
Famous quotes containing the words triple and/or bar:
“And DANTE searched the triple spheres,
Moulding nature at his will,
So shaped, so colored, swift or still,
And, sculptor-like, his large design
Etched on Alp and Apennine.”
—Ralph Waldo Emerson (18031882)
“Personally, I cant see why it would be any less romantic to find a husband in a nice four-color catalogue than in the average downtown bar at happy hour.”
—Barbara Ehrenreich (b. 1941)