In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician...

completely, however, lecturing on the paradoxes of set theory (Burali-Forti paradox, Cantor's paradox, and Russell's paradox) to a meeting of the Deutsche...

paradox and Skolem's concept of relativity to the study of the philosophy of language. One of the earliest results in set theory, published by Cantor...

must be at rest. Based on the work of Georg Cantor, Bertrand Russell offered a solution to the paradoxes, what is known as the "at-at theory of motion"...

Georg Cantor. It can be thought of as a number that is bigger than any other conceivable or inconceivable quantity, either finite or transfinite. Cantor linked...

theory, for instance Cantor's paradox and the Burali-Forti paradox, and did not believe that they discredited his theory. Cantor's paradox can actually be...

{N} } , proving Cantor's theorem. Cantor's theorem and its proof are closely related to two paradoxes of set theory. Cantor's paradox is the name given...

After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox), various axiomatic systems...

Aristotle's wheel paradox is a paradox or problem appearing in the pseudo-Aristotelian Greek work Mechanica. It states as follows: A wheel is depicted...

not itself have a cardinality, as this would lead to a paradox of the Burali-Forti type. Cantor instead said that it was an "inconsistent" collection which...

(1905), is strongly related to Cantor's diagonal argument on the uncountability of the set of real numbers. The paradox begins with the observation that...

Richard's article is translated into English. The paradox can be interpreted as an application of Cantor's diagonal argument. It inspired Kurt Gödel and Alan...

different paradox. Berry’s letter actually talks about the first ordinal that can’t be named in a finite number of words. According to Cantor’s theory such...

paradox. Algebra of sets Alternative set theory Category of sets Class (set theory) Family of sets Fuzzy set Mereology Principia Mathematica Cantor,...

When paradoxes such as Russell's paradox, Berry's paradox and the Burali-Forti paradox were discovered in Cantor's naive set theory, the issue became...

non-existence, based on different choices of axioms for set theory. Russell's paradox concerns the impossibility of a set of sets, whose members are all sets...

used by Cantor in proving his results in transfinite arithmetic are essentially the same as those used by Russell in constructing his paradox. Hence how...

Burali-Forti paradox. Georg Cantor had apparently discovered the same paradox in his (Cantor's) "naive" set theory and this become known as Cantor's paradox. Russell's...

sets, the behavior is more complex. A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities...

mathematical logic, the theory of infinite sets was first developed by Georg Cantor. Although this work has become a thoroughly standard fixture of classical...

Banach–Tarski paradox, is one of many counterintuitive results of the axiom of choice. The continuum hypothesis, first proposed as a conjecture by Cantor, was...

Banach–Tarski paradox Basel problem Bolzano–Weierstrass theorem Brouwer fixed-point theorem Buckingham π theorem (proof in progress) Burnside's lemma Cantor's theorem...

Galileo's paradox is a demonstration of one of the surprising properties of infinite sets. In his final scientific work, Two New Sciences, Galileo Galilei...

including B. Gerald Cantor, Malcolm Forbes and R. McLean Stewart. Five of Whyte's works were exhibited in the offices of Cantor-Fitzgerald and destroyed...

initiated by Georg Cantor and Richard Dedekind in the 1870s. However, the discovery of paradoxes in naive set theory, such as Russell's paradox, led to the desire...

paradox) in this treatment (Cantor's paradox), by Russell's discovery (1902) of an antinomy in Frege's 1879 (Russell's paradox), by the discovery of more...

Cantor Normal Form. Suppes, Patrick (1960), Axiomatic Set Theory, D.Van Nostrand, ISBN 0-486-61630-4. Tait, William W. (1997), "Frege versus Cantor and...

original (PDF) on 1 April 2017. Van Dalen, Dirk; Ebbinghaus, Heinz-Dieter (June 2000). "Zermelo and the Skolem Paradox". The Bulletin of Symbolic Logic...

finite is said to be countably infinite. The concept is attributed to Georg Cantor, who proved the existence of uncountable sets, that is, sets that are not...

or ℶ 1 {\displaystyle \beth _{1}} (beth-one). The Cantor set is an uncountable subset of R. The Cantor set is a fractal and has Hausdorff dimension greater...