Theory symbols and signs

Details: Category: Mathematics notes and reviews

Set theory symbols

Symbol	Symbol Name	Meaning / definition	Example
{ }	set	a collection of elements	A = {3,7,9,14}, B = {9,14,28}
A ∩ B	intersection	objects that belong to set A and set B	A ∩ B = {9,14}
A ∪ B	union	objects that belong to set A or set B	A ∪ B = {3,7,9,14,28}
A ⊆ B	subset	A is a subset of B. set A is included in set B.	{9,14,28} ⊆ {9,14,28}
A ⊂ B	proper subset / strict subset	A is a subset of B, but A is not equal to B.	{9,14} ⊂ {9,14,28}
A ⊄ B	not subset	set A is not a subset of set B	{9,66} ⊄ {9,14,28}
A ⊇ B	superset	A is a superset of B. set A includes set B	{9,14,28} ⊇ {9,14,28}
A ⊃ B	proper superset / strict superset	A is a superset of B, but B is not equal to A.	{9,14,28} ⊃ {9,14}
A ⊅ B	not superset	set A is not a superset of set B	{9,14,28} ⊅ {9,66}
2^A	power set	all subsets of A
$\mathcal{P}(A)$	power set	all subsets of A
A = B	equality	both sets have the same members	A={3,9,14}, B={3,9,14}, A=B
A^c	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 = {3,9,14}, B = {1,2,3}, A-B = {9,14}
A - B	relative complement	objects that belong to A and not to B	A = {3,9,14}, B = {1,2,3}, A-B = {9,14}
A ∆ B	symmetric difference	objects that belong to A or B but not to their intersection	A = {3,9,14}, B = {1,2,3}, A ∆ B = {1,2,9,14}
A ⊖ B	symmetric difference	objects that belong to A or B but not to their intersection	A = {3,9,14}, B = {1,2,3}, A ⊖ B = {1,2,9,14}
a∈A	element of, belongs to	set membership	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
A×B	cartesian product	set of all ordered pairs from A and B
\|A\|	cardinality	the number of elements of set A	A={3,9,14}, \|A\|=3
#A	cardinality	the number of elements of set A	A={3,9,14}, #A=3
\|	vertical bar	such that	A={x\|3<x<14}
	aleph-null	infinite cardinality of natural numbers set
	aleph-one	cardinality of countable ordinal numbers set
Ø	empty set	Ø = { }	C = {Ø}
$\mathbb{U}$	universal set	set of all possible values
$\mathbb{N}$ ₀	natural numbers / whole numbers set (with zero)	$\mathbb{N}$ ₀ = {0,1,2,3,4,...}	0 ∈ $\mathbb{N}$ ₀
$\mathbb{N}$ ₁	natural numbers / whole numbers set (without zero)	$\mathbb{N}$ ₁ = {1,2,3,4,5,...}	6 ∈ $\mathbb{N}$ ₁
$\mathbb{Z}$	integer numbers set	$\mathbb{Z}$ = {...-3,-2,-1,0,1,2,3,...}	-6 ∈ $\mathbb{Z}$
$\mathbb{Q}$	rational numbers set	$\mathbb{Q}$ = {x \| x=a/b, a,b∈ $\mathbb{Z}$ }	2/6 ∈ $\mathbb{Q}$
$\mathbb{R}$	real numbers set	$\mathbb{R}$ = {x \| -∞ < x <∞}	6.343434∈ $\mathbb{R}$
$\mathbb{C}$	complex numbers set	$\mathbb{C}$ = {z \| z=a+bi, -∞<a<∞, -∞<b<∞}	6+2i ∈ $\mathbb{C}$