Natural Neutrosophic Numbers and MOD Neutrosophic Numbers

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