## Branch 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

#### Recommended Citation

Smarandache, Florentin. "Proceedings of the First International Conference on Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability and Statistics." (2001). https://digitalrepository.unm.edu/math_fsp/269

#### Creative Commons License

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