Lemma_(mathematics)

This article is about a type of mathematical statement. For other uses, see Lemma.

In mathematics, a lemma is a proven proposition which is used as a stepping stone to a larger result rather than as a 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, such as Bézout\'s lemma, Dehn\'s lemma, Fatou\'s lemma, Gauss\'s lemma, Nakayama\'s lemma, Riesz\'s lemma, and Zorn\'s lemma. There is no formal distinction between a lemma and a theorem.

The Greek word "lemma" (λήμμα) itself means "anything which is received, such as a gift, profit, or a bribe." , The plural "lemmas" is commonly used.Higham, Nicholas J. (1998). Handbook of Writing for the Mathematical Sciences. Society for Industrial and Applied Mathematics, 16. ISBN 0898714206.  The correct Greek plural of lemma, however, is lemmata (λήμματα). 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

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• Corollary
• List of lemmas

References

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