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Set theory symbols, such as ∪ (union), ∩ (intersection), and ⊆ (subset), are fundamental mathematical notations used to represent relationships and operations within sets. These symbols play a crucial role in expressing set concepts and relationships, simplifying complex mathematical ideas into concise representations. Understanding these symbols is essential for mastering the language of set theory.** **

Symbol |
Symbol Name |
Meaning / definition |

{ } |
set |
a collection of elements |

| |
such that |
so that |

A⋂B |
intersection |
objects that belong to set A and set B |

A⋃B |
union |
objects that belong to set A or set B |

A⊆B |
subset |
A is a subset of B. set A is included in set B. |

A⊂B |
proper subset / strict subset |
A is a subset of B, but A is not equal to B. |

A⊄B |
not subset |
set A is not a subset of set B |

A⊇B |
superset |
A is a superset of B. set A includes set B |

A⊃B |
proper superset / strict superset |
A is a superset of B, but B is not equal to A. |

A⊅B |
not superset |
set A is not a superset of set B |

2A |
power set |
all subsets of A |

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 |

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-B |
relative complement |
objects that belong to A and not to B |

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∈A |
element of, belongs to |
set membership |

x∉A |
not element of |
no set membership |

(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 |
cardinality |
the number of elements of set A |

| |
vertical bar |
such that |

ℵ0 |
aleph-null |
infinite cardinality of natural numbers set |

ℵ1 |
aleph-one |
cardinality of countable ordinal numbers set |

Ø |
empty set |
Ø = {} |

U |
universal set |
set of all possible values |

ℕ0 |
natural numbers / whole numbers set (with zero) |
0 = {0,1,2,3,4,...} |

ℕ1 |
natural numbers / whole numbers set (without zero) |
1 = {1,2,3,4,5,...} |

ℤ |
integer numbers set |
{Z} = {...-3,-2,-1,0,1,2,3,...} |

ℚ |
rational numbers set |
{Q} = {x | x=a/b, a,b∈{Z} and b≠0} |

ℝ |
real numbers set |
{R} = {x | -∞ < x <∞} |

ℂ |
complex numbers set |
{C} = {z | z=a+bi, -∞<a<∞, -∞<b<∞} |

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