In mathematics, a lemma is a proven proposition which is used as a stepping stone to a larger result rather than an independent statement, in and of itself. A good stepping stone leads to many others, so some of the most powerful results in mathematics are known as lemmata: Zorn's lemma, Bézout's lemma, Gauss lemma, Fatou's lemma, Nakayama lemma, etc. There is no inherent distinction between a lemma and a theorem. Mathematics is often defined as the study of topics such as quantity, structure, space, and change. ... Proposition is a term used in logic to describe the content of assertions. ... Zorns lemma, also known as the Kuratowski-Zorn lemma, is a theorem of set theory that states: Every partially ordered set in which every chain (i. ... In number theory, Bézouts identity, named after Étienne Bézout, is a linear diophantine equation. ... In mathematics, there is more than one Gauss lemma; all are named after Carl Friedrich Gauss. ... Fatous lemma establishes an inequality relating the integral (in the sense of Lebesgue) of the limit inferior of a sequence of functions to the limit inferior of the sequence of integrals of the functions. ... In mathematics, Nakayamas Lemma is an important technical lemma in commutative algebra and algebraic geometry. ... A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. ...

The Greek word "lemma" (λημμα) itself means "anything which is received, such as a gift, profit, or a bribe." According to [1], the plural "lemmas" is commonly used. The correct Greek plural of lemma, however, is lemmata (λημματα). Both forms are used in English, although users of lemmas should be aware that Classical purists will consider their usage wrong, and users of lemmata should be aware that many readers may be unfamiliar with the term or consider its use unnecessarily pedantic. For the medical term see rigor (medicine) Rigour (American English: rigor) has a number of meanings in relation to intellectual life and discourse. ...

See also

• List of lemmas

This is a list of lemmas (i. ...

References

1. N. Higham, Handbook of writing for the mathematical sciences, Society for Industrial and Applied Mathematics, 1998 (p. 16)

This article incorporates material from Lemma on PlanetMath, which is licensed under the GFDL. PlanetMath is a free, collaborative, online mathematics encyclopedia. ...