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.
