Dense enough non-standard reals

摘要

Non-standard analysis is a branch of Mathematics introduced by Abraham Robinson in 1966[1]. In 1977, Edward Nelson gave an axiomatic approach to Non-standard analysis [2]. One of the main features of these approaches is the reduction of infiniteness to finiteness. In this paper we have come up with functions in the nonstandard setting, especially in the extended Real number system consisting of infinitesimals and infinite numbers, that are analogous with functions in classical analysis and show that non-standard numbers are dense enough to facilitate continuity of functions.