: Mathematics: identity

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identity

In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables within a certain range of validity. In other words, A = B is an identity if A and B define the same functions, and an identity is an equality between functions that are differently defined. For example, ${\\displaystyle (a+b)^{2}=a^{2}+2ab+b^{2}}$ and ${\\displaystyle \\cos ^{2}\ heta +\\sin ^{2}\ heta =1}$ are identities. Identities are sometimes indicated by the triple bar symbol $\equiv$ instead of $=$ , the equals sign. Formally, an identity is a universally quantified equality.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Identity_(mathematics))

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