Whats the difference between theorem, lemma and corollary? Both lemma and corollary are (special kinds of) theorems The "usual" difference is that a lemma is a minor theorem usually towards proving a more significant theorem Whereas a corollary is an " easy " or " evident " consequence of another theorem (or lemma)
What is the difference between lemma, axiom, definition, corollary, etc? Corollary: a true mathematical statement that follows quite directly as a consequence of a theorem or proposition (e g as a special case) Law: not very much used in pure mathematics, it is more common e g in physics to refer to a true fact about nature
graph theory - Proving corollary to Eulers formula by induction . . . I'm currently looking at two proofs to the following corollary to Euler's formula and I'm not quite seeing how the authors can make a specific assumption in their proof One proof comes from my textbook, Introduction to Graph Theory by Robin J Wilson and the other comes from Kent University about half-way down the page They essentially say
Difference between axioms, theorems, postulates, corollaries, and . . . A "Corollary" is a theorem that is usually considered an "easy consequence" of another theorem 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
Lemma, theorem, corollary. . . which one is a suitable term for an . . . Theorem, lemma,corollary seem to be a matter of taste Some very important results are known as lemmas, e g Fodor's Lemma (set theory), Urysohn' Lemma (topology) And Konig's Theorem (set theory) is a fairly minor result, but Konig's Lemma is very important
What is the word for a corollary that follows from a proof? And in writing it up, I’d simply label it Corollary, assuming that it directly followed the theorem to whose proof it was a corollary $\endgroup$ – Brian M Scott Commented Nov 5, 2012 at 21:03
Definition: Theorem, Lemma, Proposition, Conjecture and Principle etc. Definition: Theorem, Lemma, Proposition, Corollary, Postulate, Statement, Fact, Observation, Expression, Fact, Property, Conjecture and Principle Most of the time a mathematical statement is classified with one the words listed above However, I can't seem to find definitions of them all online, so I will request your aid in describe define them
Understanding a proof of corollary of Farkas lemma I'm trying to understand a proof of a corollary to the Farkas lemma in some lecture notes For completeness sake I'll first state the Farkas lemma and then the corollary + proof, as stated in these lecture notes