Lemma (mathematics)

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

In mathematics, a lemma (plural lemmata or lemmas[1]; from the Greek λήμμα, "lemma" meaning "anything which is received, such as a gift, profit, or a bribe.") 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, Poincaré's lemma, Riesz's lemma, and Zorn's lemma. There is no formal distinction between a lemma and a theorem.

[edit] See also

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[edit] References

  1. ^ Higham, Nicholas J. (1998). Handbook of Writing for the Mathematical Sciences. Society for Industrial and Applied Mathematics, 16. ISBN 0898714206. 

This article incorporates material from Lemma on PlanetMath, which is licensed under the GFDL.

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