equation that is satisfied for all values of the variables From Wikipedia, the free encyclopedia
In mathematics, the term identity has several important uses:
An equality in mathematical sense is only true under more particular conditions. For this, the symbol ≡ is sometimes used (note, however, that the same symbol can also be used for a congruence relation as well.)
A common example of the first meaning is the trigonometric identity
which is true for all real values of (since the real numbers are the domain of both sine and cosine), as opposed to
which is only true for certain values of in a subset of the domain.
The concepts of "additive identity" and "multiplicative identity" are central to the Peano axioms. The number 0 is the "additive identity" for integers, real numbers, and complex numbers. For the real numbers, for all
Similarly, The number 1 is the "multiplicative identity" for integers, real numbers, and complex numbers. For the real numbers, for all
A common example of an identity function is the identity permutation, which sends each element of the set to itself.
These meanings are not mutually exclusive; for instance, the identity permutation is the identity element in the set of permutations of under composition.
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