different between congruence vs precongruence

English

Etymology

From Middle English congruence, from Latin congruentia (“agreement”), from congru?ns, present active participle of congru? (“meet together, agree”).

Noun

congruence (plural congruences)

1. The quality of agreeing or corresponding; being suitable and appropriate.
2. (mathematics, number theory) A relation between two numbers indicating they give the same remainder when divided by some given number.
3. (mathematics, geometry) The quality of being isometric — roughly, the same measure and shape.
4. (algebra) More generally: any equivalence relation defined on an algebraic structure which is preserved by operations defined by the structure.

Synonyms

• congruency, congruity

Derived terms

• incongruence

Related terms

• congruent

Translations

See also

• residue

French

Etymology

From Latin congruentia (“agreement”), from congru?ns, present active participle of congru? (“meet together, agree”).

Pronunciation

• IPA^(key): /k??.??y.??s/
• Homophone: congruences

Noun

congruence f (plural congruences)

1. (mathematics) congruence

Related terms

• congru

Further reading

• “congruence” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).

English

Etymology

pre- +? congruence

Noun

precongruence (plural precongruences)

1. (mathematics) A congruence of a preorder