Prove the following theorem about the limit of the composition of functions.
Theorem 1 Let f : A → R and g : B → A. Suppose a is an accumulation point of
A and b is an accumulation point of B and that
i. lim t→b g(t) = a;
ii. there is a neighborhood Q of b such that for t ∈ Q ∩ B, g(t)...