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In mathematics and other fields, [a] a lemma (pl.: lemmas or lemmata) is a generally minor, proven proposition which is used to prove a larger statement. For that reason, it is also known as a "helping theorem " or an "auxiliary theorem".
One theorem is another's lemma, though the mathematical language applies a nomenclature that generally tends to call only some things lemmas and others theorems by convention, or, because the word "theorem" is used when referring to more important or valuable theorems while lemmas are seen as less theorems which support more important theorems.
In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus . [ 1 ]
In morphology and lexicography, a lemma (pl.: lemmas or lemmata) is the canonical form, [1] dictionary form, or citation form of a set of word forms. [2] In English, for example, break , breaks , broke , broken and breaking are forms of the same lexeme , with break as the lemma by which they are indexed.
This is a list of notable theorems.Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures
In mathematics, a lemma is an auxiliary theorem which is typically used as a stepping stone to prove a bigger theorem. See lemma for a more detailed explanation. Subcategories
Burnside's lemma also known as the Cauchy–Frobenius lemma; Frattini's lemma (finite groups) Goursat's lemma; Mautner's lemma (representation theory) Ping-pong lemma (geometric group theory) Schreier's subgroup lemma; Schur's lemma (representation theory) Zassenhaus lemma
A specialized theorem that is mainly used to prove another theorem is called a lemma. A proven instance that forms part of a more general finding is termed a corollary. [98] Numerous technical terms used in mathematics are neologisms, such as polynomial and homeomorphism. [99]