Ads
related to: set theory full pdf form word file generator copy and pastepdffiller.com has been visited by 1M+ users in the past month
A Must Have in your Arsenal - cmscritic
dochub.com has been visited by 100K+ users in the past month
pdfsimpli.com has been visited by 1M+ users in the past month
Search results
Results from the WOW.Com Content Network
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory — as a branch of mathematics — is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was ...
Partition of a set. A set of stamps partitioned into bundles: No stamp is in two bundles, no bundle is empty, and every stamp is in a bundle. The 52 partitions of a set with 5 elements. A colored region indicates a subset of X that forms a member of the enclosing partition. Uncolored dots indicate single-element subsets.
Family of sets. In set theory and related branches of mathematics, a family (or collection) can mean, depending upon the context, any of the following: set, indexed set, multiset, or class. A collection of subsets of a given set is called a family of subsets of , or a family of sets over More generally, a collection of any sets whatsoever is ...
The inclusive or operation in a Boolean algebra. (In ring theory it is used for the exclusive or operation) ~. 1. The difference of two sets: x ~ y is the set of elements of x not in y. 2. An equivalence relation. \. The difference of two sets: x \ y is the set of elements of x not in y.
Fundamentals. The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
Beth number. In mathematics, particularly in set theory, the beth numbers are a certain sequence of infinite cardinal numbers (also known as transfinite numbers), conventionally written , where is the Hebrew letter beth. The beth numbers are related to the aleph numbers ( ), but unless the generalized continuum hypothesis is true, there are ...
Aleph-zero. ℵ 0 (aleph-nought, aleph-zero, or aleph-null) is the cardinality of the set of all natural numbers, and is an infinite cardinal. The set of all finite ordinals, called ω or ω0 (where ω is the lowercase Greek letter omega), has cardinality ℵ 0. A set has cardinality ℵ 0 if and only if it is countably infinite, that is, there ...
General set theory. General set theory (GST) is George Boolos 's (1998) name for a fragment of the axiomatic set theory Z. GST is sufficient for all mathematics not requiring infinite sets, and is the weakest known set theory whose theorems include the Peano axioms.