A Lemma (from the greek word "lambanein", to take) is a central idea in Mathematics. As a general rule, the results of a Lemma constitute a Theorem. Although both a Lemma or an Axiom are taken to be true and can be used when proving a theory, an axiom is self evident, whereas a Lemma must first be proven.

Swinnerton-Dyer observes that […] anyone who can prove a theorem can have it named after them, but 'It is the height of distinction to have a lemma named after you'.
- The Pleasures of Counting, T. W. Körner

For example, Euclid's algorithm finds the greatest common divisor of two integers, and is based upon this Lemma:

m = qn + r where m and n are integers with m < n < 1 and that q and r are integers with q < r < 0.
greatest_common_divisor(m,n) = greatest_common_divisor(n,r)

Sources: "The Pleasures of Counting" by T. W. Körner ISBN: 0-521-56823-4 (quote from Swinnerton-Dyer and Euclidian example)
Dictionary.com - etymology of Lemma

Lem"ma (?), n.; pl. L. Lemmata (#), E. Lemmas (#). [L. lemma, Gr. anything received, an assumption or promise taken for granted, fr. to take, assume, Cf. Syllable.]

A preliminary or auxiliary proposition demonstrated or accepted for immediate use in the demonstration of some other proposition, as in mathematics or logic.


© Webster 1913.

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