Convergence of recursive functions on computers

A theorem is presented which has applications in the numerical computation of fixed points of recursive functions. If a sequence of functions { f n } is convergent on a metric space I ⊆ ℝ, then it is possible to observe this behaviour on the set ⊂ ℚ of all numbers represented in a computer. However, as is not complete, the representation of f n on is subject to an error. Then f n and f m are considered equal when its differences computed on are equal or lower than the sum of error of each f n and f m . An example is given to illustrate the use of the theorem.