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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".
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
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 ]
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.
Upload file; Search. ... Download as PDF; ... Help. In mathematics, a lemma is an auxiliary theorem which is typically used as a stepping stone to prove a ...
Courcelle's theorem (graph theory) Cousin's lemma (real analysis) Cox's theorem (probability) Craig's theorem (mathematical logic) Craig's interpolation theorem (mathematical logic) Cramér’s decomposition theorem ; Cramér's theorem (large deviations) (probability) Cramer's theorem (algebraic curves) (analytic geometry)
It is used to prove Kronecker's lemma, which in turn, is used to prove a version of the strong law of large numbers under variance constraints. It may be used to prove Nicomachus's theorem that the sum of the first n {\displaystyle n} cubes equals the square of the sum of the first n {\displaystyle n} positive integers.
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]