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In set theory, a universal set is a set which contains all objects, including itself. [1] In set theory as usually formulated, it can be proven in multiple ways that a universal set does not exist. However, some non-standard variants of set theory include a universal set.
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
A variant of set theory that includes a universal set and possibly other non-standard axioms, focusing on what can be constructed or defined positively. Polish space A Polish space is a separable topological space homeomorphic to a complete metric space pow Abbreviation for "power (set)" power "Power" is an archaic term for cardinality power ...
If A is a set, then the absolute complement of A (or simply the complement of A) is the set of elements not in A (within a larger set that is implicitly defined). In other words, let U be a set that contains all the elements under study; if there is no need to mention U, either because it has been previously specified, or it is obvious and unique, then the absolute complement of A is the ...
In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains all the entities one wishes to consider in a given situation. In set theory, universes are often classes that contain (as elements) all sets for which one hopes to prove a particular theorem.
A universal set in set theory; ... The following characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek ...
Cardinality – Definition of the number of elements in a set; Complement – Set of the elements not in a given subset; Intersection (Euclidean geometry) – Shape formed from points common to other shapes; Intersection graph – Graph representing intersections between given sets