For example, HC≡CH is a common shorthand for acetylene (systematic name: ethyne). In chemistry, the triple bar can be used to represent a triple bond between atoms. In botanical nomenclature, the triple bar denotes homotypic synonyms (those based on the same type specimen), to distinguish them from heterotypic synonyms (those based on different type specimens), which are marked with an equals sign.
Triple f bar juneau mod#
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: a ≡ b ( mod N ). Particularly, in geometry, it may be used either to show that two figures are congruent or that they are identical. 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 ≈). 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.
Alternatively, in some texts ⇔ is used with this meaning, while ≡ is used for the higher-level metalogical notion of logical equivalence, according to which two formulas are logically equivalent when all models give them the same value. This is a binary operation whose value is true when its two arguments have the same value as each other. It can refer to the if and only if connective, also called material equivalence. In logic, it is used with two different but related meanings.
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