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# Set Theory Symbols

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University of Guelph

Statistics

STAT 2060

Tony Desmond

Fall

Description

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

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