1. The problem statement, all variables and given/known data Let f : A --> R be a function, and let c in A be an isolated point of A. Prove that f is continuous at c 2. Relevant equations 3. The attempt at a solution I'm kind of confused by this problem.... if c is an isolated point, then the limit doesn't exist. So I can't really use the fact that a function is continuous at c if for all epsilon>0 there exists a delta>0 such that whenever |x-c|<delta, it follows that |f(x)-f(c)|<epsilon. Any hints would be great!