Equivalence class
Set
| context | $X$ |
| context | $x\in X$ |
| context | $\sim\in\text{Equiv}(X) $ |
| definiendum | $ y\in [x]_\sim $ |
| postulate | $y\sim x$ |
Ramifications
Discussion
For some combinatorics on the number of possible equivalence classes, see Bell number (Wikipedia).
Reference
Wikipedia: Equivalence class