hat is a relation?

A relation is a set of ordered pairs that shows how elements are related.

Example:
(1, 1), (2, 2), (3, 3)

What is an equivalence relation?

An equivalence relation is a relation that satisfies three properties:

1. Reflexive

2. Symmetric

3. Transitive

If a relation has all three, it is an equivalence relation.

Why equivalence relations matter

They group elements that are considered “equal in some way,” even if they are not exactly the same number.

Example:
Two numbers are related if they leave the same remainder when divided by 3.