Lemma (mathematics)

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”) or helping theorem 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 can lead to many others. Some powerful results in mathematics are known as lemmata, such as Bézout's lemma, Dehn's lemma, Euclid's lemma, Farkas' lemma, Fatou's lemma, Gauss's lemma, Greendlinger's lemma, Itō's lemma, Jordan's lemma, Nakayama's lemma, Poincaré's lemma, Riesz's lemma, Schwarz's lemma, Urysohn's lemma, Yoneda'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

Look up lemma in Wiktionary, the free dictionary.

• Corollary
• Fundamental lemma
• List of lemmas
• Theorem terminology

References

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.