**Cantor's paradox** — In set theory, Cantor s paradox is the theorem that there is no greatest cardinal number, so that the collection of infinite sizes is itself infinite. Furthermore, it follows from this fact that this collection is not a set but a proper class; in … Wikipedia

**Cantor's diagonal argument** — An illustration of Cantor s diagonal argument for the existence of uncountable sets. The sequence at the bottom cannot occur anywhere in the list of sequences above. Cantor s diagonal argument, also called the diagonalisation argument, the… … Wikipedia

**Skolem's paradox** — is the mathematical fact that every countable axiomatisation of set theory in first order logic, if consistent, has a model that is countable, even if it is possible to prove, from those same axioms, the existence of sets that are not countable.… … Wikipedia

**Russell's paradox** — Part of the foundations of mathematics, Russell s paradox (also known as Russell s antinomy), discovered by Bertrand Russell in 1901, showed that the naive set theory of Frege leads to a contradiction.It might be assumed that, for any formal… … Wikipedia

**Galileo's paradox** — is a demonstration of one of the surprising properties of infinite sets.In his final scientific work, the Two New Sciences , Galileo made two apparently contradictory statements about the positive whole numbers. First, some numbers are perfect… … Wikipedia

**Hilbert's paradox of the Grand Hotel** — is a mathematical paradox about infinite sets presented by German mathematician David Hilbert (1862–1943). The Paradox of the Grand Hotel Consider a hypothetical hotel with infinitely many rooms, all of which are occupied that is to say every… … Wikipedia

**Paradox** — For other uses, see Paradox (disambiguation). Further information: List of paradoxes A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition. Typically,… … Wikipedia

**Georg Cantor** — Infobox Scientist name = Georg Ferdinand Ludwig Cantor image width=225px caption = birth date = birth date|1845|3|3 birth place = Saint Petersburg, Russia death date = death date and age|1918|1|6|1845|3|3 death place = Halle, Germany residence =… … Wikipedia

**Turing's proof** — First published in January 1937 with the title On Computable Numbers, With an Application to the Entscheidungsproblem , Turing s proof was the second proof of the assertion (Alonzo Church proof was first) that some questions are undecidable :… … Wikipedia

**Banach–Tarski paradox** — The Banach–Tarski paradox is a theorem in set theoretic geometry which states that a solid ball in 3 dimensional space can be split into several non overlapping pieces, which can then be put back together in a different way to yield two identical … Wikipedia