Kongruentsi

Kongruentsi is a term used in several languages to denote the idea of congruence: a relationship of compatibility or agreement between two objects under a specified relation. In mathematics, kongruentsi is most commonly encountered in modular arithmetic: for integers a, b and a positive integer n, a is congruent to b modulo n if n divides the difference a − b. This relation is denoted a ≡ b (mod n) and partitions the integers into equivalence classes. Congruence is an equivalence relation: reflexive, symmetric, and transitive. It allows arithmetic to be performed on residues, with rules such as adding or multiplying congruences: if a ≡ b (mod n) and c ≡ d (mod n) then a + c ≡ b + d (mod n) and ac ≡ bd (mod n). Generalizations extend to rings and to congruences defined by ideals, enabling modular arithmetic in number theory, cryptography, and coding theory.

In linguistics, kongruentsi can refer to grammatical agreement, where words or phrases change form to accord with others in person, number, gender, or case. This is known as concord in many languages; subject–verb agreement is a common example. Congruence in morphology ensures that adjectives, determiners, and verbs align with the nouns they modify.

In logic and computer science, a congruence relation is an equivalence relation compatible with a structure, allowing the formation of quotient structures and the use of congruence closure in automated reasoning.