Describing a sequence of real-valued functions on a given domain which converge at the same rate for all points of the domain. More precisely, a sequence of functions fn on a domain D converges uniformly to the function f if for every ε > 0 and for every x in D, there is an integer N for which |fn(x) − f(x)| < ε for all n > N. In particular, the sequence converges pointwise on D. Uniform convergence generalizes naturally to functions taking values in a metric space.