Search results
Results from the WOW.Com Content Network
Bertrand's postulate and a proof; Estimation of covariance matrices; Fermat's little theorem and some proofs; Gödel's completeness theorem and its original proof; Mathematical induction and a proof; Proof that 0.999... equals 1; Proof that 22/7 exceeds π; Proof that e is irrational; Proof that π is irrational
The simplest and most common form of mathematical induction infers that a statement involving a natural number n (that is, an integer n ≥ 0 or 1) holds for all values of n. The proof consists of two steps: The base case (or initial case): prove that the statement holds for 0, or 1.
ZF stands for Zermelo–Fraenkel set theory, and DC for the axiom of dependent choice.. Solovay's theorem is as follows. Assuming the existence of an inaccessible cardinal, there is an inner model of ZF + DC of a suitable forcing extension V[G] such that every set of reals is Lebesgue measurable, has the perfect set property, and has the Baire property.
[1] A mathematical proof is a deductive argument for a mathematical statement, ... (2018), Book of Proof, Richard Hammack, ISBN 978-0-9894721-3-5. External links
All horses are the same color is a falsidical paradox that arises from a flawed use of mathematical induction to prove the statement All horses are the same color. [1] There is no actual contradiction, as these arguments have a crucial flaw that makes them incorrect.
Ne’Kiya Jackson and Calcea Johnson have published a paper on a new way to prove the 2000-year-old Pythagorean theorem. Their work began in a high school math contest.
Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for all members of the domain. [2] [3] Some sources use the term existentialization to refer to existential quantification. [4] Quantification in general is covered in the article on quantification (logic).
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!