Numbers and Models , Standard and Nonstandard
نویسنده
چکیده
The following is a somewhat extended manuscript for a talk at the " Algebra Days " , May 2008, in Antalya. I talked about my personal recollections of Abraham Robinson.
منابع مشابه
Nonstandard Numbers for Qualitative Decision Making
The consideration of nonstandard models of the real numbers and the definition of a qualitative ordering on those models provides a generalization of the principle of maximization of expected utility. It enables the decider to assign probabilities of different orders of magnitude to different events or to assign utilities of different orders of magnitude to different outcomes. The properties of...
متن کاملNonstandard finite difference schemes for differential equations
In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...
متن کاملA New Approach to Nonstandard Analysis
In this paper, we propose a new approach to nonstandard analysis without using the ultrafilters. This method is very simple in practice. Moreover, we construct explicitly the total order relation in the new field of the infinitesimal numbers. To illustrate the importance of this work, we suggest comparing a few applications of this approach with the former methods.
متن کاملA nonstandard set theory in the ∈-language
Wedemonstrate that a comprehensive nonstandard set theory can be developed in the standard ∈-language. As an illustration, a nonstandard Law of Large Numbers is obtained.
متن کاملHyperreals and Their Applications
NSA can be introduced in multiple ways. Instead of choosing one option, these notes include three introductions. Section 1 is best-suited for those who are familiar with logic, or who want to get a flavor of model theory. Section 2 focuses on some common ingredients of various axiomatic approaches to NSA, including the star-map and the Transfer principle. Section 3 explains the ultrapower const...
متن کامل