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Transcript
Set Theory Symbols List of set symbols of set theory and probability. Table of set theory symbols A∩B Example Symbol Name Meaning / definition a collection of A = {3,7,9,14}, set elements B = {9,14,28} objects that belong to intersection A ∩ B = {9,14} set A and set B A∪B union Symbol {} A⊆B A⊂B A⊄B A⊇B A⊃B A⊅B 2A objects that belong to A ∪ B = set A or set B {3,7,9,14,28} subset has fewer subset elements or equal to {9,14,28} ⊆ {9,14,28} the set proper subset / subset has fewer strict subset elements than the set {9,14} ⊂ {9,14,28} left set not a subset of not subset {9,66} ⊄ {9,14,28} right set set A has more superset elements or equal to {9,14,28} ⊇ {9,14,28} the set B proper superset set A has more {9,14,28} ⊃ {9,14} / strict superset elements than set B set A is not a superset not superset {9,14,28} ⊅ {9,66} of set B power set all subsets of A power set all subsets of A equality both sets have the same members Ac complement all the objects that do not belong to set A A\B relative complement A-B relative complement A=B A={3,9,14}, B={3,9,14}, A=B A = {3,9,14}, objects that belong to B = {1,2,3}, A and not to B A-B = {9,14} objects that belong to A = {3,9,14}, A and not to B B = {1,2,3}, A-B = {9,14} A = {3,9,14}, B = {1,2,3}, A ∆ B = {1,2,9,14} A = {3,9,14}, B = {1,2,3}, 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 ⊖ B = {1,2,9,14} a∈A element of set membership x∉A not element of no set membership (a,b) ordered pair A×B cartesian product |A| cardinality #A cardinality aleph-null aleph-one Ø empty set universal set 0 1 real numbers set A={3,9,14}, 1 ∉ A collection of 2 elements set of all ordered pairs from A and B the number of A={3,9,14}, |A|=3 elements of set A the number of A={3,9,14}, #A=3 elements of set A infinite cardinality of natural numbers set cardinality of countable ordinal numbers set Ø={} C = {Ø} set of all possible values natural numbers / whole 0 = {0,1,2,3,4,...} numbers set (with zero) natural numbers / whole 1 = {1,2,3,4,5,...} numbers set (without zero) integer = {...-3,-2,numbers set 1,0,1,2,3,...} rational numbers set A={3,9,14}, 3 ∈ A = {x | x=a/b, a,b∈ } = {x | -∞ < x <∞} 0∈ 0 6∈ 1 -6 ∈ 2/6 ∈ 6.343434 ∈ complex numbers set = {z | z=a+bi, ∞<a<∞, -∞<b<∞} 6+2i ∈