Lemma (mathematics)
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It has been suggested that this article or section be merged with lemma (logic). (Discuss) Proposed since December 2011. |
In mathematics, a lemma (plural lemmata or lemmas[1] from the Greek λῆμμα (lemma, “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 of interest by itself. There is no formal distinction between a lemma and a theorem, only one of intention – see Theorem#Terminology. However Couchman makes a distinction between a lemma and a theorem when it comes to Set Theory
A good stepping stone leads to many others, so some of the most powerful results in mathematics are known as lemmas, 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, Itō's lemma and Zorn's lemma. While these results originally seemed too simple or too technical to warrant independent interest, they have turned out to be central to the theories in which they occur.
[edit] See also
| Look up lemma in Wiktionary, the free dictionary. |
[edit] References
- ^ Higham, Nicholas J. (1998). Handbook of Writing for the Mathematical Sciences. Society for Industrial and Applied Mathematics. pp. 16. ISBN 0898714206.
[edit] 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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