define lemma? with examples
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In mathematics, a "helping theorem" or lemma (plural lemmas or lemmata) is a proven proposition which is used as a stepping stone to a larger result rather than as a statement of interest by itself.[1] The word derives from the Ancient Greek λῆμμα ("anything which is received, such as a gift, profit, or a bribe").
good stepping stone can lead to many others. Some powerful results in mathematics are known as lemmas, 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, Vitali covering 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.
good stepping stone can lead to many others. Some powerful results in mathematics are known as lemmas, 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, Vitali covering 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.
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in mathematics are helping theorem or Lemma is a proven proposition which is used as a stepping stone of larger result rather than a statement of interest by itself .
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emankaushik:
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