Would you say a congruence class such as $[0]_{4}, [1]_{4}, [2]_{4},$ and $[3]_{4}$ an example of Equivalence classes since:
the set of all elements of $\{..., -8, -4, 0, 4, 8,...\}$ is related to $[0]_{4}$ because of $0$ $mod$ $4$.
The set of all elements of $\{..., -7, -3, 1, 5, 9,...\}$ is related to $[1]_{4}$ because of $1$ $mod$ $4$.
The set of all elements of $\{..., -6, -2, 2, 6, 10,...\}$ is related to $[2]_{4}$ because of $2$ $mod$ $4$.
The set of all elements of $\{..., -5, -1, 3, 7, 11,...\}$ is related to $[3]_{4}$ because of $3$ $mod$ $4$.
My claim: All of these are examples of Equivalence classes.
My question is, am I on the correct path of understanding what Equivalence Classes are? Or am I making a mistake here? Is this a correct understand of Equivalence Classes are? Thank you so very much.