Mathematics and Statistics Faculty and Staff Publications

Document Type

Book

Publication Date

2001

Abstract

In 1960s Abraham Robinson has developed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, that rigorously defines the infinitesimals. Informally, an infinitesimal is an infinitely small number. Formally, x is said to be infinitesimal if and only if for all positive integers n one has xxx < 1/n. Let &>0 be a such infinitesimal number. The hyper-real number set is an extension of the real number set, which includes classes of infinite numbers and classes of infinitesimal numbers. Let’s consider the non-standard finite numbers 1+ = 1+&, where “1” is its standard part and “&” its non-standard part, and –0 = 0-&, where “0” is its standard part and “&” its non-standard part. Then, we call ]-0, 1+[ a non-standard unit interval. Obviously, 0 and 1, and analogously nonstandard numbers infinitely small but less than 0 or infinitely small but greater than 1, belong to the non-standard unit interval.

Publisher

Xiquan - Gallup

ISSN

1-931233-67-5

Language (ISO)

English

Keywords

Neutrosophy, Neutrosophic Logic, neutrosophic Set

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

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