selfidentical

Self-identical describes the property of being identical to oneself; an object or statement that is true or congruent with its own reference. In logic and philosophy, it relates to the law of identity: every entity is identical to itself, formalized as for any x, x = x. This reflexive axiom underpins mathematical equality and logical deduction, and it distinguishes identity from other relations such as similarity or equivalence.

In mathematics, identity expresses a fixed, unavoidable sameness. The statement a = a holds for all a in any given domain. The identity function id, defined by id(x) = x, is a standard example of a self-identical object: it maps every element to itself. In set theory and algebra, equality is treated as an equivalence relation that is reflexive, symmetric, and transitive, reinforcing the concept of self-identity.

In computing and computer science, the idea of identity is often separated from value. An object has an identity distinct from its current state or content, and programming languages provide mechanisms to reference the object's identity (for example, via pointers or a built-in identity or "this" reference). Self-identical patterns arise in recursive definitions and self-referential data structures.

In everyday use, self-identical is often synonymous with the broader notion of being the same as oneself across time or contexts, a foundational idea in theories of personal and numerical identity. See also: law of identity, reflexivity, identity function, self-similarity.