In mathematics, a lemma (plural lemmata or lemmas^[1]; from the Greek λήμμα, "lemma" meaning "anything which is received, such as a gift, profit, or a bribe. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly ") is a proven proposition which is used as a stepping stone to a larger result rather than as a statement in-and-of itself. In Logic and Philosophy, proposition refers to either (a the content or Meaning of a meaningful Declarative sentence A good stepping stone leads to many others, so some of the most powerful results in mathematics are known as lemmata, such as Bézout's lemma, Dehn's lemma, Fatou's lemma, Gauss's lemma, Nakayama's lemma, Poincaré's lemma, Riesz's lemma, and Zorn's lemma. In Number theory, Bézout's identity or Bézout's lemma is a linear Diophantine equation. In Mathematics Dehn's lemma asserts that a Piecewise-linear map of a disk into a 3-manifold, with the map's singularity set in the disc's interior In Mathematics, Fatou's lemma establishes an Inequality relating the Integral (in the sense of Lebesgue) of the limit inferior of Gauss's lemma can mean any of several lemmas named after Carl Friedrich Gauss: Gauss's lemma (polynomial Gauss's lemma In Mathematics, Nakayama's lemma is an important technical lemma in Commutative algebra and Algebraic geometry. In Mathematics, especially Vector calculus and Differential topology, a closed form is a Differential form α whose differential is Riesz's lemma is an lemma in Functional analysis. It specifies (often easy to check conditions which guarantee that a Subspace in a Normed linear Zorn's lemma, also known as the Kuratowski-Zorn lemma, is a proposition of Set theory that states Every Partially ordered set in which There is no formal distinction between a lemma and a theorem. In Mathematics, a theorem is a statement proven on the basis of previously accepted or established statements

See also

• Corollary
• List of lemmas

References

This article incorporates material from Lemma on PlanetMath, which is licensed under the GFDL. PlanetMath is a free, collaborative online Mathematics Encyclopedia.