 First, in the 1960s Abraham Robinson, using methods of mathematical logic, created nonstandard analysis, an extension of mathematical analysis embracing both “infinitely large” and infinitesimal numbers in which the usual laws of the arithmetic of real numbers continue to hold, an idea which, in essence, goes back to Leibniz. Here by an infinitely large number is meant one which exceeds every positive integer; the reciprocal of any one of these is infinitesimal in the sense that, while being nonzero, it is smaller than every positive fraction \(1/n\). Much of the usefulness of nonstandard analysis stems from the fact that within it every statement of ordinary analysis involving limits has a succinct and highly intuitive translation into the language of infinitesimals.