Abraham robinson developed nonstandard analysis, in which the reals are rigor ously extended to include in nitesimal numbers and in nite numbers. In this thesis we will look at three nonstandard proofs of big theorems in functional analysis. Non standard analysis grew out of robinson s attempt to resolve the contradictions posed by infinitesimals within calculus. This material is covered thoroughly in robinson s book nonstandard analysis. The next result demonstrates the remarkable feature of non standard analysis to reduce and sometimes even to eliminate completely the number of quantifiers. Nonstandard analysis was originated in the early 1960s by the mathematician abraham robinson. Model theory deals with the construction of concrete objects structures which satisfy a given collection of statements. We then enter functional analysis by discussing banach and hilbert spaces. Considered by many to be abraham robinson s magnum opus, this book offers an explanation of the development and applications of non standard analysis by the mathematician who founded the subject. In nonstandard analysis, however, all that need be done is to replace in. At any rate, the use of infinitesimals was widespread during the formative stages of the differential and integral calculus.
Nonstandard analysis grew out of robinsons attempt to resolve the contradictions posed by infinitesimals within calculus. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers. Though it is not necessary to use it, it can bring great elegance to a proof. Considered by many to be abraham robinsons magnum opus, this book offers an explanation of the development and applications of nonstandard analysis by the mathematician who founded the subject. Please read our short guide how to send a book to kindle.