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Set Theory (What is a Set? (A set is a well defined collection of unique…
Set Theory
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Numeric Sets
N represents the set of natural numbers- numbers that we use for counting 1, 2, 3..
Z represents the set of integers. These are the natural numbers plus their negative counterparts and zero.
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R represents the set of real numbers. Real numbers are the rational numbers plus the irrational numbers.
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Set Relationships
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A proper subset
Set A is a proper subset of B if all elements of A are contained in B, but B has at least one element that is not in A.
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Cardinality of sets
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An infinite set is a set that is not finite. It is not possible to list out all the elements of an infinite set.
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Set Theory
A set is a structure, representing an unordered collection of zero or more distinct objects.
Set theory deals with operations between, relations among, and statements about sets,
Set Theory Notation
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Defining Sets
Sets can be defined two ways:
- by set enumeration - listing each element.
- by set comprehension- defining the rules for membership.
A = {1, 2, 3, 4} - set enumeration
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Universal Sets
The universal set is the set of all things pertinent to a given discussion and is designated by the symbol U.
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Properties of Sets
The two most important properties of sets are that: 1) Order of elements is irrelevant
2) Elements are unique
Example A = {1, 2, 3}
{1, 3, 2}
{2, 1, 3}
