Lemma

Lemma may refer to:

See also

Lemma (botany)

Lemma is a phytomorphological term used in botany referring to a part of the spikelet of grasses (Poaceae). It is the lowermost of two chaff-like bracts enclosing the grass floret. It often bears a long bristle called an awn, and may be similar in form to the glumes - chaffy bracts at the base of each spikelet. It is usually interpreted as a bract but it has also been interpreted as one remnant (the abaxial) of the three members of outer perianth whorl (the palea may represent the other two members, having been joined together).

A lemma's shape, their number of veins, whether they are awned or not, and the presence or absence of hairs are particularly important characters in grass taxonomy.

Lemma (mathematics)

In mathematics, a "helping theorem" or lemma (plural lemmata or lemmas) from the Ancient 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.

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 theorem – a step in the direction of proof, so to speak.

Well-known lemmas

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, Schur'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.