Mathematical Lemma

A Mathematical Lemma is a proven mathematical statement that is presented in order to prove another mathematical statement, such as a mathematical theorem.

• Context:
  • It can be more complex to Prove than a Mathematical Proposition.
  • It can be less complex to Prove than a Mathematical Theorem.
• See: Mathematical Corollary.

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References

2009

• WordNet.
  • a subsidiary proposition that is assumed to be true in order to prove another proposition
  • the lower and stouter of the two glumes immediately enclosing the floret in most Gramineae
  • the heading that indicates the subject of an annotation or a literary composition or a dictionary entry
• In mathematics, a lemma (plural lemmata or lemmas; from the Greek λήμμα, "lemma" meaning "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 in-and-of itself. ...
  • en.wikipedia.org/wiki/Lemma_(mathematics)
• In informal logic and argument mapping, a lemma is simultaneously a contention for premises below it and a premise for a contention above it.
  • en.wikipedia.org/wiki/Lemma_(logic)
• Farkas' lemma is a result in mathematics used amongst other things in the proof of the Karush-Kuhn-Tucker theorem in nonlinear programming. ...
  • en.wikipedia.org/wiki/Lemma_(Farkas)
• In linguistics a lemma (plural lemmas or lemmata) is the canonical form of a lexeme.
  • en.wikipedia.org/wiki/Lemma_(linguistics)
• http://en.wiktionary.org/wiki/Lemmas
  • A proposition proved or accepted for immediate use in the proof of some other proposition;
  • A lexeme; all the inflected forms of a term
• http://planetmath.org/encyclopedia/Lemma.html
  • There is no technical distinction between a lemma, a proposition, and a theorem. A lemma is a proven statement, typically named a lemma to distinguish it as a truth used as a stepping stone to a larger result rather than an important statement in and of itself. Of course, some of the most powerful statements in mathematics are known as lemmas, including Zorn's Lemma, Bezout's Lemma, Gauss' Lemma, Fatou's lemma, etc., so one clearly can't get too much simply by reading into a proposition's name.
  • Even less well-defined is the distinction between a proposition and a theorem. Many authors choose to name results only one or the other, or use both more or less interchangeably. A partially standard set of nomenclature is to use the term proposition to denote a significant result that is still shy of deserving a proper name. In contrast, a theorem under this format would represent a major result, and would often be named in relation to mathematicians who worked on or solved the problem in question.
  • The Greek word “lemma” 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. The Greek “Theoria” means “view, or vision" and is clearly linguistically related to the word “theatre.” The apparent relation is that a theorem is a mathematical fact which you see to be true (and can now show others!).
  • A somewhat more distinct concept (though still subject to author discretion) is that of a corollary, which is a result that can be considered an immediate consequence of a previous theorem (typically, the preceding theorem in the text).

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