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In the left hand sides of the following identities, is the L eft most set and is the R ight most set. Whenever necessary, both L and R {\displaystyle L{\text{ and }}R} should be assumed to be subsets of some universe set X , {\displaystyle X,} so that L ∁ := X ∖ L and R ∁ := X ∖ R . {\displaystyle L^{\complement }:=X\setminus L{\text ...
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".
Download QR code; Print/export Download as PDF; Printable version; In other projects ... List of set identities and relations – Equalities for combinations of sets;
In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [1] As an example, " is less than " is a relation on the set of natural numbers ; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3 ), and likewise between 3 and 4 (denoted as 3 < 4 ), but not between the ...
The simple theorems in the algebra of sets are some of the elementary properties of the algebra of union (infix operator: ∪), intersection (infix operator: ∩), and set complement (postfix ') of sets. These properties assume the existence of at least two sets: a given universal set, denoted U, and the empty set, denoted {}.
A set is described by listing elements separated by commas, or by a characterizing property of its elements, within braces { }. [5] Since sets are objects, the membership relation can relate sets as well, i.e., sets themselves can be members of other sets. A derived binary relation between two sets is the subset relation, also called set inclusion.
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The power object of a set A is given by its power set, and the exponential object of the sets A and B is given by the set of all functions from A to B. Set is thus a topos (and in particular cartesian closed and exact in the sense of Barr). Set is not abelian, additive nor preadditive. Every non-empty set is an injective object in Set. Every ...