Lemma (mathematics)

From the Ancient Greek λῆμμα, (perfect passive εἴλημμαι) something received or taken. Thus, something taken for granted in an argument. == Comparison with theorem ==

There is no formal distinction between a lemma and a theorem, only one of intention (see Theorem terminology). However, a lemma can be considered a minor result whose sole purpose is to help prove a more substantial theorem – a step in the direction of proof. == Well-known lemmas ==

Some powerful results in mathematics are known as lemmas, first named for their originally minor purpose. These include, among others: • Bézout's lemma • Burnside's lemma • Dehn's lemma • Euclid's lemma • Farkas' lemma • Fatou's lemma • Gauss's lemma (any of several named after Carl Friedrich Gauss) • Greendlinger's lemma • Itô's lemma • Jordan's lemma • Lovász local lemma • Nakayama's lemma • Noether normalization lemma • Poincaré's lemma • Riesz's lemma • Schur's lemma • Schwarz's lemma • Sperner's lemma • Urysohn's lemma • Vitali covering lemma • Yoneda's lemma • Zariski's lemma • Zorn's lemma While these results originally seemed too simple or too technical to warrant independent interest, they have eventually turned out to be central to the theories in which they occur. == See also ==