Playground

Equivalence Binner

Define an equivalence relation on a set and watch the elements auto-bin into equivalence classes. Drag elements between bins to explore.

A/R={[a]R∣a∈A},  [a]R={b∣(a,b)∈R}A / R = \{[a]_R \mid a \in A\},\ \ [a]_R = \{b \mid (a,b) \in R\}
Setup
Equivalence classes (8)
valid partition
[·]_01 items
1
[·]_11 items
2
[·]_21 items
3
[·]_31 items
4
[·]_41 items
5
[·]_51 items
6
[·]_61 items
7
[·]_71 items
8
Quotient set A/R has 8 classes · each class has at least one element.