Pointwise convergence refers to a type of convergence for sequences of functions. A sequence of functions f_n converges pointwise to a function f on a set D if, for every point x in D, the sequence of real numbers f_n(x) approaches f(x) as n increases. This means that for each individual point, the values of the functions get closer to the value of the limiting function. In mathematical terms, pointwise convergence is defined as: for every x in D and for every ε > 0, there exists an integer N such that for all n ≥ N, the absolute difference |f_n(x) - f(x)| < ε. This concept is important in analysis and helps in understanding how functions behave as they are approximated by sequences.