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## Set Theory Symbols

### Set Theory Symbols :

Set theory symbols, such as ∪ (union), ∩ (intersection), and ⊆ (subset), are fundamental mathematical notations used to represent relationships and operations within sets. These symbols play a crucial role in expressing set concepts and relationships, simplifying complex mathematical ideas into concise representations. Understanding these symbols is essential for mastering the language of set theory.

### Table of Set Theory Symbols

 Symbol Symbol Name Meaning / definition { } set a collection of elements | such that so that A⋂B intersection objects that belong to set A and set B A⋃B union objects that belong to set A or set B A⊆B subset A is a subset of B. set A is included in set B. A⊂B proper subset / strict subset A is a subset of B, but A is not equal to B. A⊄B not subset set A is not a subset of set B A⊇B superset A is a superset of B. set A includes set B A⊃B proper superset / strict superset A is a superset of B, but B is not equal to A. A⊅B not superset set A is not a superset of set B 2A power set all subsets of A P(A) power set all subsets of A P(A) power set all subsets of A ℙ(A) power set all subsets of A A=B equality both sets have the same members Ac complement all the objects that do not belong to set A A' complement all the objects that do not belong to set A A\B relative complement objects that belong to A and not to B A-B relative complement objects that belong to A and not to B A∆B symmetric difference objects that belong to A or B but not to their intersection A⊖B symmetric difference objects that belong to A or B but not to their intersection a∈A element of, belongs to set membership x∉A not element of no set membership (a,b) ordered pair collection of 2 elements A×B cartesian product set of all ordered pairs from A and B |A| cardinality the number of elements of set A #A cardinality the number of elements of set A | vertical bar such that ℵ0 aleph-null infinite cardinality of natural numbers set ℵ1 aleph-one cardinality of countable ordinal numbers set Ø empty set Ø = {} U universal set set of all possible values ℕ0 natural numbers / whole numbers set (with zero) 0 = {0,1,2,3,4,...} ℕ1 natural numbers / whole numbers set (without zero) 1 = {1,2,3,4,5,...} ℤ integer numbers set {Z} = {...-3,-2,-1,0,1,2,3,...} ℚ rational numbers set {Q} = {x | x=a/b, a,b∈{Z} and b≠0} ℝ real numbers set {R} = {x | -∞ < x <∞} ℂ complex numbers set {C} = {z | z=a+bi, -∞

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