## Mathematics and Statistics Faculty and Staff Publications

#### Document Type

Book

#### Publication Date

2015

#### Abstract

In this book authors answer the question proposed by Florentin Smarandache “Does there exist neutrosophic numbers which are such that they take values differently and behave differently from I; the indeterminate?”. We have constructed a class of natural neutrosophic numbers m 0I , m xI , m yI , m zI where m 0I × m 0I = m 0I , m xI × m xI = m xI and m yI × m yI = m yI and m yI × m xI = m 0I and m zI × m zI = m 0I . Here take m = 12, x = 4, y = 9 and z = 6. For more refer chapter one of this book. Thus we have defined or introduced natural neutrosophic numbers using Zm under division. Further there are more natural neutrosophic numbers in the MOD interval [0, m). This concept is thoroughly analysed in chapter two.

#### Publisher

EuropaNova, Brussels

#### ISSN

978-1-59973-366-1

#### Language (ISO)

English

#### Keywords

neutrosophic numbers, neutrosophic logic, number theory

#### Recommended Citation

W.B. Vasantha Kandasamy, K. Ilanthenral, & F. Smarandache. Natural Neutrosophic Numbers and MOD Neutrosophic Numbers. Brussels: EuropaNova ASBL, 2015.

#### Creative Commons License

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

#### Included in

Algebra Commons, Algebraic Geometry Commons, Analysis Commons, Applied Mathematics Commons, Number Theory Commons, Other Mathematics Commons