Set Theory Symbols

List of set symbols of set theory and probability.

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} | | \| | such that | so that | A = {x \| x∈ $\mathbb{R}$ , x<0} | | 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} | | 2A | power set | all subsets of A | | | $\mathcal{P}(A)$ | 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 | A={3,9,14},B={3,9,14},A=B | | 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 = {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×B = {(a,b)\|a∈A , b∈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} | | ℵ0 | aleph-null | infinite cardinality of natural numbers set | | | ℵ1 | aleph-one | cardinality of countable ordinal numbers set | | | Ø | empty set | Ø = {} | A = Ø | | $\mathbb{U}$ | universal set | set of all possible values | | | ℕ0 | natural numbers / whole numbers set (with zero) | $\mathbb{N}$ 0 = {0,1,2,3,4,...} | 0 ∈ $\mathbb{N}$ 0 | | ℕ1 | natural numbers / whole numbers set (without zero) | $\mathbb{N}$ 1 = {1,2,3,4,5,...} | 6 ∈ $\mathbb{N}$ 1 | | ℤ | integer numbers set | $\mathbb{Z}$ \= {...-3,-2,-1,0,1,2,3,...} | \-6 ∈ $\mathbb{Z}$ | | ℚ | rational numbers set | $\mathbb{Q}$ \= {x \| x\=a/b, a,b∈ $\mathbb{Z}$ and b≠0} | 2/6 ∈ $\mathbb{Q}$ | | ℝ | real numbers set | $\mathbb{R}$ \= {x \| -∞ < x <∞} | 6.343434 ∈ $\mathbb{R}$ | | ℂ | complex numbers set | $\mathbb{C}$ \= {z \| z=a+bi, -∞<a<∞, -∞<b<∞} | 6+2_i_ ∈ $\mathbb{C}$ |

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Set Theory Symbols

Set Theory Symbols

Set Theory Symbols

Table of set theory symbols

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