identycznoci

Identyczność, although often written identycznosc without diacritics in Polish, denotes the relation of sameness or numerical identity between two terms: two references designate the same object. In formal contexts it is called the identity relation.

In mathematics and logic, identity is the equality relation on a given universe. It is reflexive (every object is identical to itself), symmetric, and transitive. The statements a = a are always true; if a = b then b = a, and if a = b and b = c then a = c. The identity relation helps distinguish objects from merely sharing properties. The identity function id_X: X → X, defined by id(x) = x, is a basic example.

In philosophy, identity concerns what it takes for two descriptions to refer to the same object. Leibniz's Law states that if x and y are identical, then every property of x is a property of y. Debates examine identity over time, persistence, and the criteria by which objects survive change, such as personal identity (the continuity of self) and object identity under physical or psychological continuity.

In computing and language, identity often contrasts with equality. In many programming languages, identity means reference equality (the same memory location) rather than structural or value equality. In linguistics and everyday speech, identyczność is used in contexts ranging from mathematics to precise referential use.