Lemma (mathematics)

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The word lemma has a different meaning in logic and in linguistics.

In mathematics, a lemma is a proven proposition which is used as a stepping stone to a larger result rather than an independent 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 Zorn's lemma, Bézout's lemma, Gauss's lemma, Fatou's lemma, and Nakayama lemma. There is no formal distinction between a lemma and a theorem.

The Greek word "lemma" (λήμμα) itself means "anything which is received, such as a gift, profit, or a bribe." According to [1], the plural "lemmas" is commonly used. The correct Greek plural of lemma, however, is lemmata (λήμματα). Both forms are used in English, although users of lemmas should be aware that Classical purists will consider their usage wrong, and users of lemmata should be aware that many readers may be unfamiliar with the term or consider its use unnecessarily pedantic.