Lemma (mathematics)

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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, Urysohn's lemma, Dehn's lemma, Fatou's lemma, Gauss's lemma, Nakayama's lemma, Poincaré's lemma, Riesz's lemma, Schwarz's lemma and Zorn's lemma. There is no formal distinction between a lemma and a theorem, only one of usage and convention.

[edit] See also

Look up lemma in Wiktionary, the free dictionary.

• Corollary
• List of lemmas

[edit] References

[edit] External links

• Doron Zeilberger, Opinion 82: A Good Lemma is Worth a Thousand Theorems

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

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