Sequences

Abstract

Early records of classical Greek mathematics show a marked aversion for any methods involving infinite processes. For centuries this remained the prevailing attitude among mathematicians. Indeed, there was no significant change until the time of Sir Isaac Newton. In 1669 he composed his famous treatise De Analysi per aequationes numero terminorum infinitas (published in 1711) which included an account of his work on infinite series as well as the beginnings of calculus. Because of the work of Newton the use of infinite processes became regarded as a legitimate mathematical tool. In time, it was recognised that careful rules needed to be developed governing the use of such infinite processes and the calculus in order to ensure the validity of the final results, and thus real analysis came into being. The rigorous subject as we know it today stems, in the main, from the work of eighteenth and nineteenth-century mathematicians on the continent. Many years of work by some of the most outstanding mathematicians of the last few centuries have produced the final polished version.