Sets: Hierarchy
Set concepts
Elementary collections
unstructured collections
set
bag, multiset
list, sequence
(unordered list)
notion of sets
fundamental set properties
disorder
uniqueness of elements
multiplicity of elements
set (member) element vs object
Set representation
intensional representation
extensional representation
Set notation
Roster form
Set builder notation
Set cardinality
Finite set
the empty set vs nonempty set
the empty set
nonempty set
singleton set
unordered pair
Infinite sets
Infinite enumerable set
Infinite innumerable set
Set equality
intensional equality
extensional equality
equal sets
equivalent sets
equinumerousity
Universal set
Operations on sets
Set union
Set intersection
Set difference
Set complement (negation)
Cartesian product, cross/dot product
Set properties and operations
Cardinal number
Unordered pair
Ordered pair
Set covering
Set partitioning
Number of proper subsets
Bell Numbers
Natural numbers in terms of sets
Algebraic properties of sets
Set identities
Idempotency
Set relations
inclusion relation
subset, superset
proper subset, proper superset
membership relation
indexed set
family of sets
Basic set relations
Set membership
Set member
Set paradox
Richard's paradox
Russell's paradox
Set inclusion
Disjoint sets
pair-wise disjoint sets
Overlapping sets
subset, superset
proper subset, proper superset
Power set
set product, Cartesian product
ordered pair
Fundamental sets
The set of natural numbers
The set of integers
The set of rational numbers
The set of real numbers
The set of complex numbers
Mathematical theories
Set theory
naive set theory
axiomatic set theory
axioms of set theory
Relation theory
Order theory
Domain theory
Function theory
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