Difference between revisions of "Category:Set Theory"

A

• A cap (B-C) = (A cap B) - C
• A pair of identical elements is a singleton
• A-(A-B) = A cap B
• Arity
• Axiom of foundation
• Axiom of regularity
• Axiom schema of replacement

B

• Bijection
• Bijective
• Binary relation

C

• Canonical projection of an equivalence relation
• Canonical projection of the equivalence relation
• Cardinality
• Cartesian product
• Commutativity of intersection
• Complement
• Complementation
• Completely invariant under
• Composition of functions
• Constant function
• Constant map
• Constant mapping
• Correspondence
• Cover

D

• De Morgan's laws
• Disjoint
• Disjoint in
• Disjoint in a set
• Disjoint union
• Disjoint union (set)
• Distributivity of intersections across unions

E

• Empty set
• Empty-set
• Emptyset
• Equivalence class
• Equivalence classes
• Equivalence classes are either equal or disjoint
• Equivalence relation
• Equivalence relation induced by a function
• Notes:Equivalence relations
• Equivalence relations
• Equivalent conditions to a set being saturated with respect to a function
• Equivalent conditions to a set being saturated with respect to a map
• Every bijection yields an inverse function
• Every injection yields a bijection onto its image
• Every surjective map gives rise to an equivalence relation
• Extension

F

• Factoring a function through the projection of an equivalence relation induced by that function yields an injection
• Fibre
• Fibre (map)
• Function
• Function factorisation
• Function factorisation theorem
• Function terminology
• Template:Function terminology navbox
• Functions

G

• Graph

H

• Hereditary
• Hereditary class of sets

H cont.

• Hereditary set
• Hereditary set system
• Hereditary system
• Hereditary system generated by

I

• Identity map
• If the composition of two functions is a bijection then the initial map is injective and the latter map is surjective
• Implies-subset relation
• Index of elementary set theory equalities
• Indicator function
• Inductive set
• Infimum
• Injection
• Injective
• Integer division
• Integers
• Intersection is commutative
• Invariant of an equivalence relation
• Invariant under

L

• Liminf (sequence of sets)
• Limit of increasing sequence of sets
• Limsup (sequence of sets)
• Limsup and liminf
• Limsup and liminf (sequence of sets)
• Logical implication

M

• Map
• Mapping
• Mappings
• Min/max
• Modulo operation
• Modulo operator
• Monotone
• Monotonic
• Motivation for set theory axioms

N

• Non-empty
• Non-empty in

O

• Order terminology
• Ordered pair
• Ordered pairs
• Ordering

P

• Partial order
• Partial ordering
• Partial-function
• Partition (abstract algebra)
• Passing to the quotient
• Passing to the quotient (function)
• Talk:Passing to the quotient (function)/Induced is surjective iff function is surjective
• Passing-to-the-quotient (function)
• Permutation
• Permutation of a set
• Permutation on a set
• Poset
• Positive and negative parts of a function
• Power-set
• Pre-image (map)
• Predicate
• Preorder
• Preordering
• Preset
• Properties of the pre-image of a map

Q

• Quotient (function)
• Quotient by an equivalence relation
• Quotient by the equivalence relation

R

• Rational numbers
• Real numbers
• Reflexive relation
• Relation
• Relations
• Replacement axiom
• Restriction
• Restriction (function)
• Rewriting for-all and exists within set theory

S

• Saturated
• Saturated (map)
• Saturated set with respect to a function
• Saturated with respect to a function
• Sequence
• Set
• Set complement
• Set function
• Set subtraction
• Set theory axioms
• Set-subtraction
• Sets
• Singleton
• Singleton (set theory)
• Singleton (set theory)/Definition
• Strict partial order
• Strict partial ordering
• Sub-sequence
• Subsequence
• Subsequence/Definition
• Subset
• Successor function
• Successor of a set
• Successor set
• Surjection
• Surjective
• Surjectivity
• Symmetric difference
• Symmetric relation

T

• The 2 foundational ways of counting
• The 6 primitives of counting
• The diagonal (set)
• The domain, range and field of a relation exist
• The integers
• The intersection of sets is a subset of each set
• The reals
• The relationship between logical implication and the subset relation
• There is no set of all sets
• Transitive relation
• Tuples
• Types of set algebras

U

• Union
• Union of subsets is a subset of the union

W

• Well-ordered set
• Well-ordering