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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. Its main uses are in mathematics and logic.
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
The symbol ≡ is used in science and mathematics with several different meanings. It may refer to the following: ... Equivalence relation, often denoted using a ...
See also ∝ for a less ambiguous symbol. ≡ 1. Denotes an identity; that is, an equality that is true whichever values are given to the variables occurring in it. 2. In number theory, and more specifically in modular arithmetic, denotes the congruence modulo an integer. 3. May denote a logical equivalence.
The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title.
Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one. Decimal representations are rounded or padded to 10 places if the values are known.
So, + and are two different expressions that represent the same number. This is the meaning of the equality 3 + 2 = 5. {\displaystyle 3+2=5.} A more complicated example is given by the expression ∫ a b x d x {\textstyle \int _{a}^{b}xdx} that can be evaluated to b 2 2 − a 2 2 . {\textstyle {\frac {b^{2}}{2}}-{\frac {a^{2}}{2}}.}
The symbol is used to denote negation. For example, if P(x) is the predicate "x is greater than 0 and less than 1", then, for a domain of discourse X of all natural numbers, the existential quantification "There exists a natural number x which is greater than 0 and less than 1" can be symbolically stated as: