Category:Equivalence Relations
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This category contains results about Equivalence Relations.
Definitions specific to this category can be found in Definitions/Equivalence Relations.
Let $\RR$ be a relation on a set $S$.
Let $\RR$ be:
- $(1): \quad$ reflexive
- $(2): \quad$ symmetric
- $(3): \quad$ transitive
Then $\RR$ is an equivalence relation on $S$.
Subcategories
This category has the following 19 subcategories, out of 19 total.
A
C
- Congruence Modulo Subgroup (8 P)
E
F
Q
R
T
U
- Union of Equivalences (3 P)
W
- Well-Defined Relations (2 P)
Pages in category "Equivalence Relations"
The following 53 pages are in this category, out of 53 total.
C
- Cardinality of Set of Induced Equivalence Classes of Injection
- Cardinality of Set of Induced Equivalence Classes of Surjection
- Cartesian Product of Equivalence Relations
- Cauchy Sequences in Vector Spaces with Equivalent Norms Coincide
- Composite of Inverse of Mapping with Mapping
- Composite of Mapping with Inverse
- Connected Equivalence Relation is Trivial
- Construction of Inverse Completion
- Convergent Sequences in Vector Spaces with Equivalent Norms Coincide
- Correspondence Theorem (Set Theory)
- Cross-Relation Equivalence Classes on Natural Numbers are Cancellable for Addition
D
E
- Equivalence iff Diagonal and Inverse Composite
- Equivalence Induced on Preordering defines Ordering
- Equivalence of Definitions of Equivalence Relation
- Equivalence of Definitions of Saturated Set Under Equivalence Relation
- Equivalence of Definitions of Saturation Under Equivalence Relation
- Equivalence Relation is Circular
- Equivalence Relation is Congruence iff Compatible with Operation
- Equivalent Characterizations of Finer Equivalence Relation
R
- Reflexive Circular Relation is Equivalence
- Reflexive Euclidean Relation is Equivalence
- Relation Induced by Mapping is Equivalence Relation
- Relation Induced by Partition is Equivalence
- Relation Induced by Quotient Set is Equivalence
- Relation is Equivalence iff Reflexive and Circular
- Relation Isomorphism is Equivalence Relation
- Relation Isomorphism Preserves Equivalence Relations
- Relation Partitions Set iff Equivalence
- Relation Partitions Set iff Equivalence/Proof
- Renaming Mapping from Set of Mappings on Single Element
- Renaming Mapping is Bijection
- Renaming Mapping is Well-Defined
- Restriction of Equivalence Relation is Equivalence