18.099: Problem Set 1

Due: Wednesday, September 10.

1. Let n be a positive integer. Show that

1 + 2 + 3 + ⋯ + n = \frac{n(n + 1)}{2}.

2. Let f: A → B and g: B → C be maps between sets, and suppose that the composition g∘f: A → C is a bijection. Does it follow that f is injective, surjective, or bijective? Same question for g.