Chess/Bishop/Equivalence classes/Example

In chess, a bishop can move diagonally and arbitrarily far in every direction. Two squares (positions) on a chess board are called bishop-equivalent if it is possible to reach, starting from one square, by finitely many bishop moves, the other square. This is an equivalence relation on the chess board. Moving diagonally, the color of the position does not change; therefore, a bishop standing on a white square will always stay on a white square. Moreover, a bishop, standing on a white square, can reach every white square. Hence, there are only two equivalence classes: the white squares and the black squares; accordingly, we talk about the light-squared and the dark-squared bishop (this is not the color of the piece).