Lemma (mathematics)

In mathematics, a lemma (plural lemmata or lemmas) 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.

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, Euclid's lemma, Farkas' lemma, Fatou's lemma, Gauss's lemma, Greendlinger's lemma, Jordan'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.

See also

• Corollary
• Fundamental lemma
• List of lemmas

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 Creative Commons Attribution/Share-Alike License.