Abstract or Additional Information
Nonstandard Analysis is generally considered to have little utility. So we'll keep it brief. After a discussion of the origins of the idea of infinitesimals, we will see some details of the modern ultra-power construction. We will briefly discuss Abraham Robinson's construction based on "the compactness theorem". We will re-state some standard analytic results in non-standard terms. Finally, we will see a case of similar techniques proving useful in non-standard metric fixed point theory. This case will provide a positive example for the claim that "every mathematical structure has a nonstandard model from which knowledge of the original structure can be gained by applications of the appropriate Transfer Principle."