Second hint

I feel like a second hint would be good here. Maybe writing A = {a_1, a_2, ...} and/or to clarify that B \subsetneq A and |A| = |B| are not a contradiction for infinite sets.

I think the second is unnecessary (I hope by now in this course students have realized that infinity and one less than infinity are still both infinite.

You're right. The new second hint is helpful.