The Cauchy criterion and real limiting processes
A. M. Cohen · International Journal of Mathematical Education in Science and Technology · 1987
The paper develops the principal theorems on limits of convergent sequences starting from the Cauchy criterion. The traditional definition causes problems to students as it presupposes the existence of a limit before checking that a sequence converges. The Cauchy criterion, in addition to overcoming this problem, also leads to more precise results. The convergence of sequences generated on a computer is also examined and practical criteria for terminating iterations are compared and analysed.