Equivalence Classes Discussion

(The following is/are the initial prompt(s) for an online discussion; students may have posted responses, and prompts for further discussion may have been added, but these things are not shown.)

Equivalence relations create a structure of “equivalence classes” on their domains/ranges, which can be an interesting way to organize that set. This discussion helps build intuition for what equivalence classes are.

Think about some game you like to play (e.g., a card game, board game, maybe some athletic game), and the objects in that game (e.g., the cards, positions on a game board, maybe positions or pieces of equipment on a playing field). Describe one or more equivalence relations on these objects. Or maybe new equivalence relations you see in the objects someone else has suggested. Then identify the equivalence classes that those relations partition the objects into. How do those “real world” classes reflect the mathematical properties that equivalence classes are supposed to have?