Category:Elementary 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

B

• Bijection

C

• Canonical projection of an equivalence relation
• Canonical projection of the equivalence relation
• Completely invariant under
• Composition of functions
• Constant function
• Constant map
• Constant mapping

D

• Disjoint
• Disjoint in
• Disjoint in a set
• Disjoint union
• Disjoint union (set)
• Distributivity of intersections across unions

E

• Empty set
• Empty-set
• Emptyset
• Equivalence classes are either equal or disjoint
• Equivalence relation induced by a function
• 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

E cont.

• Every surjective map gives rise to an equivalence relation

F

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

G

• Greater than or equal to
• Greater than or equal to/Epsilon form

H

• Hereditary
• Hereditary class of sets
• 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
• Index of elementary set theory equalities
• Integers
• Intersection is commutative
• Invariant of an equivalence relation
• Invariant under

M

• Mappings
• Maps

N

• Non-empty
• Non-empty in

O

• Ordered pairs

P

• Partial-function

P cont.

• Passing to the quotient (function)
• Passing-to-the-quotient (function)
• Pre-image
• Pre-image (map)
• Properties of classes of sets closed under set-subtraction
• Properties of the pre-image of a map

Q

• Quotient by an equivalence relation
• Quotient by the equivalence relation

R

• Restriction (function)

S

• Saturated
• Saturated (map)
• Saturated set with respect to a function
• Saturated with respect to a function
• Set-subtraction
• Sets
• Singleton
• Singleton (set theory)
• Singleton (set theory)/Definition
• Subset of
• Successor of a set
• Surjectivity

T

• The 2 foundational ways of counting
• The 6 primitives of counting
• The integers
• The intersection of two sets is non-empty if and only if there exists a point in one set that is in the other set
• Tuples