nonempty set
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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
Set theory — This article is about the branch of mathematics. For musical set theory, see Set theory (music). A Venn diagram illustrating the intersection of two sets. Set theory is the branch of mathematics that studies sets, which are collections of objects … Wikipedia
nonempty — ˌ adjective : not empty ; specifically : containing at least one element nonempty sets * * * /non emp tee/, adj. Math. (of a set, group, collection, etc.) containing at least one element. [1935 40; NON + EMPTY … Useful english dictionary
nonempty — adjective a) Not empty, containing something. b) Describing a set that contains at least one element and is therefore distinct from the empty set … Wiktionary
nonempty — /non emp tee/, adj. Math. (of a set, group, collection, etc.) containing at least one element. [1935 40; NON + EMPTY] * * * … Universalium
Directed set — In mathematics, a directed set (or a directed preorder or a filtered set) is a nonempty set A together with a reflexive and transitive binary relation ≤ (that is, a preorder), with the additional property that every pair of elements has an upper… … Wikipedia
Intersection (set theory) — Intersections of the Greek, Latin and Russian alphabet (upper case graphemes) (The intersection of Greek and Latin letters is used for the Greek licence plates.) … Wikipedia
Partition of a set — In mathematics, a partition of a set X is a division of X into non overlapping parts or blocks or cells that cover all of X . More formally, these cells are both collectively exhaustive and mutually exclusive with respect to the set being… … Wikipedia
Infinite set — In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. Some examples are: * the set of all integers, {..., 1, 0, 1, 2, ...}, is a countably infinite set; and * the set of all real numbers… … Wikipedia
Open set — Example: The points (x, y) satisfying x2 + y2 = r2 are colored blue. The points (x, y) satisfying x2 + y2 < r2 are colored red. The red points form an open set. The blue points form a closed set. The union of the red and blue points is a… … Wikipedia
Stationary set — In mathematics, particularly in set theory and model theory, there are at least three notions of stationary set:Classical notionIf kappa is a cardinal of uncountable cofinality, Csubseteqkappa, and C intersects every club in kappa, then C is… … Wikipedia
