My university teach nothing in this covid period, so I was really relax for the online exams. But suddenly they notified us the exam be conducted in offline mode. I was freaked out.....I don't know nothing, thank you so much sir. I wish you were my teacher. Thanks!!
I found one example is not correct: m~n iff m-n is divisibke by 3. Right to left direction is okay, but the opposite doesn't hold because equality or equinumerosity is equivalence relation, so even though a relation is equivalent, that doesn't imply that the relation is being divisible by 3.
I agree, it is a little confusing. It is appropriate to say "for any m, n in Z" here since you are allowed to "compare" any two values of m and n to see if they are equivalent. In fact, if you watch the video on the relationship between equivalence relations and partitions, then you will see that equivalence relations carve up the set into a bunch of non-overlapping subsets.
