What's the difference between theorem, lemma and corollary?
Lemma — a minor result whose sole purpose is to help in proving a theorem. It is a stepping stone on the path to proving a theorem. It is a stepping stone on the path to proving a theorem. Very occasionally lemmas can take on a life of their own (Zorn’s lemma, Urysohn’s lemma, Burnside’s lemma, Sperner’s lemma).
Definition: Theorem, Lemma, Proposition, Conjecture and Principle …
Theorem vs. Lemma is totally subjective, but typically lemmas are used as components in the proof of a theorem. Propositions are perhaps even weaker, but again, totally subjective. A conjecture is a statement which requires proof, should be proven, and is not proven.
Lemma/Proposition/Theorem, which one should we pick?
Lemma - technical result used in the proof of the theorem, which is claimed as original and proved, but the main interest in which lies its use in the proof of one or more theorems. Corollary - a specialization of a just presented theorem, in terms more likely to be useful in practice, or of intuitive interest.
real analysis - What is the difference between lemma, axiom, …
2018年3月31日 · Lemma: a true statement that can be proved (proceeding from other true statements or from the axioms) and that is immediately (or almost immediately) used to prove something more important (a theorem / proposition).
请解释一下这些语料库语言学概念：type，token, lemma，word …
lemma 词目 一个实词可能会有很多种inflections，比如be，就会有am,is, are,was,were等等屈折变化形式，be就可以称作词目 word family 词族 在语言发展的过程中积累很多声音和意义相通或相近的同源词，不同的同源词可以一组一组的分开，每组自成系统，通常称为词族。
Proof of rigidity lemma - Mathematics Stack Exchange
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A proof of Jones lemma - Mathematics Stack Exchange
2020年3月3日 · A proof of Jones lemma. Ask Question Asked 4 years, 9 months ago. Modified 4 years, 9 months ago. Viewed ...
How to prove the square lemma? - Mathematics Stack Exchange
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terminology - Difference between axioms, theorems, postulates ...
2010年10月25日 · What is or is not a corollary is entirely subjective. Sometimes what an author thinks is a 'corollary' is deemed more important than the corresponding theorem. (The same goes for "Lemma"s, which are theorems that are considered auxiliary to proving some other, more important in the view of the author, theorem). A "hypothesis" is an assumption made.
category theory - Proof of the Nine Lemma using the Snake …
2020年4月4日 · Lemma (Snake Lemma). Given a commutative diagram Given a commutative diagram where the rows are exact, there is an exact sequence $$ 0\longrightarrow\ker\lambda\longrightarrow\ker\mu\longrightarrow\ker\nu\overset{\delta}\longrightarrow{\rm coker}~\lambda\longrightarrow{\rm coker}~\mu\longrightarrow{\rm coker}~\nu\longrightarrow0 $$