ABSTRACT

Questions about limits go back to the ancient Greeks. The Greeks really did not understand limits (witness Zeno’s paradoxes). The question of limits arose even more intensely in the development of calculus. Isaac Newton did not understand limits, and neither did Leibniz. It took the combined efforts of a number of nineteenth-century mathematical geniuses-including Cauchy, Riemann, Dirichlet, Weierstrass, and others-to finally nail down the concept of limit. Here we present the fruits of their efforts.