Lemma (mathematics)

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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.

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.

See also

• List of lemmas

References

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

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