Symbols related to set theory

The symbols in this reference may be used anywhere in text.

Set operators

Description
Symbol
Grafstate code
Meaning
Union
⋃
\u
A⋃B ≝ {x∣x∈A⋁x∈B}
Intersection
⋂
\n
A⋂B ≝ {x∣x∈A⋀x∈B}
Set minus
-
-
A - B ≝ {x∣x∈A⋀x∉B}
Symmetric difference
Δ
\D
A Δ B={x∣x∈A ⊕ x∈B}
= (A - B) ⋃ (B - A)
Cartesian product
\*
A B={(x,y)∣x∈A⋀y∈B}
Power set
℘()
\P()
℘(A)={S∣S ⊆ A}

Statements relating two sets

Description
Symbol
Grafstate code
Meaning
Subset of
⊆
\subset
A ⊆ B ⟺ ∀x[x∈A⟶x∈B]
Not a subset of
⊈
\!subset
A ⊈ B ⟺ ∃x∈A[x∉B]
Proper subset of
⊊
\psubset
A ⊊ B ⟺ A ⊆ B⋀A ≠ B
Superset of
⊇
\supset
A ⊇ B ⟺ ∀x[x∈B⟶x∈A]
Not a superset of
⊉
\!supset
A ⊉ B ⟺ ∃x∈B[x∉A]
Proper superset of
⊋
psupset
A ⊋ B ⟺ A ⊇ B⋀A¬=B

Other symbols related to sets

Description
Symbol
Grafstate code
Contained in
∈
\in
Not contained in
∉
\!in
Contains
∋
\has
Does not contain
∌
\!has
Empty set
∅
{}
\0
{}
Natural numbers
ℕ
\\GSSYMbtick35;N
Integers
ℤ
\\GSSYMbtick35;Z
Rational numbers
ℚ
\\GSSYMbtick35;Q
Real numbers
ℝ
\\GSSYMbtick35;R
Complex numbers
ℂ
\\GSSYMbtick35;C
aleph
ℵ
\aleph
aleph-null
ℵ0
\al0
aleph-one
ℵ1
\al1