A set is a arsenal of things, normally numbers. We can list each aspect (or "member") the a collection inside curly brackets favor this:

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Common Symbols supplied in set Theory

Symbols conserve time and an are when writing. Below are the most common collection symbols

In the instances C = 1, 2, 3, 4 and also D = 3, 4, 5


Symbol definition example
Set: a arsenal of elements 1, 2, 3, 4
A ∪ B Union: in A or B (or both) C ∪ D = 1, 2, 3, 4, 5
A ∩ B Intersection: in both A and also B C ∩ D = 3, 4
A ⊆ B Subset: every facet of A is in B.

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3, 4, 5 ⊆ D
A ⊂ B Proper Subset: every facet of A is in B,but B has more elements. 3, 5 ⊂ D
A ⊄ B Not a Subset: A is not a subset that B 1, 6 ⊄ C
A ⊇ B Superset: A has same elements as B, or more 1, 2, 3 ⊇ 1, 2, 3
A ⊃ B Proper Superset: A has B"s elements and more 1, 2, 3, 4 ⊃ 1, 2, 3
A ⊅ B Not a Superset: A is no a superset that B 1, 2, 6 ⊅ 1, 9
Ac Complement: elements not in A Dc = 1, 2, 6, 7When = 1, 2, 3, 4, 5, 6, 7
A − B Difference: in A yet not in B 1, 2, 3, 4 − 3, 4 = 1, 2
a ∈ A Element of: a is in A 3 ∈ 1, 2, 3, 4
b ∉ A Not facet of: b is no in A 6 ∉ 1, 2, 3, 4
Ø Empty set = 1, 2 ∩ 3, 4 = Ø
Universal Set: collection of all possible values(in the area the interest)
P(A) Power Set: all subsets of A P(1, 2) = , 1, 2, 1, 2
A = B Equality: both sets have actually the exact same members 3, 4, 5 = 5, 3, 4
A×B Cartesian Product(set that ordered pairs from A and B) 1, 2 × 3, 4= (1, 3), (1, 4), (2, 3), (2, 4)
|A| Cardinality: the number of elements of collection A |3, 4| = 2
| Such that n = 1, 2, 3,...
: Such that n : n > 0 = 1, 2, 3,...
For All ∀x>1, x2>x For all x better than 1x-squared is better than x
There Exists ∃ x | x2>x there exists x such thatx-squared is better than x
Therefore a=b ∴ b=a
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Natural numbers 1, 2, 3,... Or 0, 1, 2, 3,...

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Integers ..., −3, −2, −1, 0, 1, 2, 3, ...
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Rational Numbers
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Algebraic Numbers
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Real Numbers
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Imaginary Numbers 3i
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Complex Numbers 2 + 5i