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Identity ○꠹｜Definition｜1st｜20251119205401-00-⌔

Identity (mathematics) - Wikipedia

Identity (mathematics)

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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 domain of discourse.¹² 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, $(a+b{)}^2=a^2+2ab+b^2$ and ${\cos }^2\theta +{\sin }^2\theta =1$ are identities.³ Identities are sometimes indicated by the triple bar symbol ≡ instead of =, the equals sign.⁴ Formally, an identity is a universally quantified equality.

Printed 2026-06-28.

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Footnotes

1. Equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Equation&oldid=32613 ↩

2. Pratt, Vaughan, “Algebra”, The Stanford Encyclopedia of Philosophy (Winter 2022 Edition), Edward N. Zalta & Uri Nodelman (eds.), URL: https://plato.stanford.edu/entries/algebra/#Laws ↩

3. “Mathwords: Identity”. www.mathwords.com. Retrieved 2019-12-01. ↩

4. “Identity – math word definition – Math Open Reference”. www.mathopenref.com. Retrieved 2019-12-01. ↩

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