# Subset

In mathematics, especially in set theory, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment.

Read more about SubsetDefinitions, The Symbols ⊂ and ⊃, Examples, Other Properties of Inclusion

### Other articles related to "subset":

List Of Forcing Notions - Definitions
... A subset D of P is called dense if for every p P there is some q D with q ≤ p ... A filter on P is a nonempty subset F of P such that if p < q and p F then q F, and if p F and q F then there is some r F with r ≤ p and r ≤ q ... A subset G of P is called generic over M if it is a filter that meets every dense subset of P in M ...
Subgroup Test
... is a theorem that states that for any group, a nonempty subset of that group is itself a group if the inverse of any element in the subset multiplied with ... The two-step subgroup test is a similar theorem which requires the subset to be closed under the operation and taking of inverses ...
Subset - Other Properties of Inclusion
... This can be illustrated by enumerating S = {s1, s2, …, sk} and associating with each subset T ⊆ S (which is to say with each element of 2S) the k-tuple from {0,1}k of which ...
Loomis–Whitney Inequality - A Special Case
... The Loomis–Whitney inequality can be used to relate the Lebesgue measure of a subset of Euclidean space to its "average widths" in the coordinate directions ... Let E be some measurable subset of and let be the indicator function of the projection of E onto the jth coordinate hyperplane ... Loomis–Whitney inequality also holds if we consider a finite subset of Euclidean space and replace Lebesgue measure by counting measure ...
List Of Forcing Notions - Shooting A Fast Club
... For S a stationary subset of we set is a closed sequence from S and C is a closed unbounded subset of, ordered by iff end-extends and and ... In, we have that is a closed unbounded subset of S almost contained in each club set in V ...