infinity cardinality

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• Infinity — In mathematics, infinity is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things: an infinite number of terms ) but it is a different type of number from the real numbers. Infinity is related to… …   Wikipedia

• infinity — /in fin i tee/, n., pl. infinities. 1. the quality or state of being infinite. 2. something that is infinite. 3. infinite space, time, or quantity. 4. an infinite extent, amount, or number. 5. an indefinitely great amount or number. 6. Math. a.… …   Universalium

• Cardinality — In mathematics, the cardinality of a set is a measure of the number of elements of the set . For example, the set A = {1, 2, 3} contains 3 elements, and therefore A has a cardinality of 3. There are two approaches to cardinality ndash; one which… …   Wikipedia

• Axiom of infinity — In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of infinity is one of the axioms of Zermelo Fraenkel set theory. Formal statement In the formal language of the Zermelo Fraenkel axioms,… …   Wikipedia

• Aleph number — In the branch of mathematics known as set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets. They are named after the symbol used to denote them, the Hebrew letter aleph (aleph).The… …   Wikipedia

• Exponentiation — Exponent redirects here. For other uses, see Exponent (disambiguation). Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent (or power) n. When n is a positive integer, exponentiation… …   Wikipedia

• set theory — the branch of mathematics that deals with relations between sets. [1940 45] * * * Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its… …   Universalium

• 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

• Cardinal number — This article describes cardinal numbers in mathematics. For cardinals in linguistics, see Names of numbers in English. In mathematics, cardinal numbers, or cardinals for short, are generalized numbers used to measure the cardinality (size) of… …   Wikipedia

• 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

• 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