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, Couchman'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. However Couchman makes a distinction between a lemma and a theorem when it comes to Set Theory.
See also
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References
- ^ Higham, Nicholas J. (1998). Handbook of Writing for the Mathematical Sciences. Society for Industrial and Applied Mathematics. pp. 16. ISBN 0898714206.
External links
This article incorporates material from Lemma on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
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