Lemma (mathematics)
In
It is also used generally in scholarship and philosophy.[4][5]
Etymology
From the Ancient Greek λῆμμα, (perfect passive εἴλημμαι) something received or taken. Thus something taken for granted in an argument. [6]
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.[3]
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
- Nakayama's 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
- 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
- Axiom
- Corollary
- Co-premise
- Fundamental lemma
- Inference objection
- List of lemmas
- Objection
- Porism
- Theorem
- Theorem terminology
References
- ISBN 0-89871-420-6.
- ^ "Definition of lemma | Dictionary.com". www.dictionary.com. Retrieved 2019-11-28.
- ^ a b Richeson, Dave (2008-09-23). "What is the difference between a theorem, a lemma, and a corollary?". David Richeson: Division by Zero. Retrieved 2019-11-28.
- ^ [1] "Lemma." Merriam-Webster.com Dictionary, Merriam-Webster.
- ISBN 9781498555739p. 47
- ^ "Oxford English Dictionary". www.oed.com. Oxford University Press. Retrieved 26 April 2023.
External links
This article incorporates material from Lemma on