Category:Equivalence Classes
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This category contains results about Equivalence Classes.
Let $S$ be a set.
Let $\RR \subseteq S \times S$ be an equivalence relation on $S$.
Let $x \in S$.
Then the equivalence class of $x$ under $\RR$ is the set:
- $\eqclass x \RR = \set {y \in S: \tuple {x, y} \in \RR}$
Subcategories
This category has the following 3 subcategories, out of 3 total.
E
Pages in category "Equivalence Classes"
The following 11 pages are in this category, out of 11 total.
E
- Element in its own Equivalence Class
- Equivalence Class Equivalent Statements
- Equivalence Class holds Equivalent Elements
- Equivalence Class is not Empty
- Equivalence Class is Unique
- Equivalence Class of Element is Subset
- Equivalence Class of Fixed Element
- Equivalence Class of Fixed Element/Corollary
- Equivalence Class of Isometries is Subset of Equivalence Class of Homeomorphisms
- Equivalence Classes are Disjoint