Let f: D->R and let c be an element of D. We say that f is continuous at c if for every e>0 there exists a q>0 such that |f(x) - f(c)| < e whenever |x-c| < q and x is an elemend of D.
If f si continuous at each point of a subset S of D, then f is said to be continuous on S. If f is continuous on its domain D, then f is said to be continuous