Math 104 Assignment 8 common mistakes

• Many people assumed uniform continuity instead of merely continuity on problem 1.
• Also on problem 1, some people went from a sequence $(a_n)_n$ with the property that $d(f(a_n), f(a)) \lt \epsilon$ whenever $d(a_n, a) \lt \delta$ to the claim that $d(f(x), f(a)) \lt \epsilon$ whenever $d(x, a) \lt \delta$, which of course does not immediately follow for $x$ which do not occur in the sequence.