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Set Symbols
Set Symbols
A set is a collection of things, usually numbers. We can list each element (or "member") of a set inside curly brackets like this:
Common Symbols Used in Set Theory
Symbols save time and space when writing. Here are the most common set symbols
In the examples C = {1, 2, 3, 4} and D = {3, 4, 5}
Symbol Meaning Example { } Set: a collection of elements {1, 2, 3, 4} A ⪠B Union: in A or B (or both) C ⪠D = {1, 2, 3, 4, 5} A â© B Intersection: in both A and B C â© D = {3, 4} A â B Subset: every element of A is in B. {3, 4, 5} â D A â B Proper Subset: every element of A is in B,
but B has more elements. {3, 5} â D A â B Not a Subset: A is not a subset of B {1, 6} â C A â B Superset: A has same elements as B, or more {1, 2, 3} â {1, 2, 3} A â B Proper Superset: A has B's elements and more {1, 2, 3, 4} â {1, 2, 3} A â
B Not a Superset: A is not a superset of B {1, 2, 6} â
{1, 9} Ac Complement: elements not in A Dc = {1, 2, 6, 7}
When = {1, 2, 3, 4, 5, 6, 7} A â B Difference: in A but not in B {1, 2, 3, 4} â {3, 4} = {1, 2}
a â A Element of: a is in A 3 â {1, 2, 3, 4} b â A Not element of: b is not in A 6 â {1, 2, 3, 4} Ã Empty set = {} {1, 2} â© {3, 4} = Ã Universal Set: set of all possible values
(in the area of interest)
P(A) Power Set: all subsets of A P({1, 2}) = { {}, {1}, {2}, {1, 2} } A = B Equality: both sets have the same members {3, 4, 5} = {5, 3, 4} AÃB Cartesian Product
(set of ordered pairs from A and B) {1, 2} Ã {3, 4}
= {(1, 3), (1, 4), (2, 3), (2, 4)} |A| Cardinality: the number of elements of set A |{3, 4}| = 2 | Such that { n | n > 0 } = {1, 2, 3,...} : Such that { n : n > 0 } = {1, 2, 3,...} â For All âx>1, x2>x
For all x greater than 1
x-squared is greater than x â There Exists â x | x2>x
There exists x such that
x-squared is greater than x â´ Therefore a=b â´ b=a
Natural Numbers {1, 2, 3,...} or {0, 1, 2, 3,...} Integers {..., â3, â2, â1, 0, 1, 2, 3, ...} Rational Numbers Algebraic Numbers Real Numbers Imaginary Numbers 3i Complex Numbers 2 + 5i
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