In this book authors name the interval [0, m); 2 ≤ m ≤ ∞ as mod interval. We have studied several properties about them but only here on wards in this book and forthcoming books the interval [0, m) will be termed as the mod real interval, [0, m)I as mod neutrosophic interval, [0,m)g; g2 = 0 as mod dual number interval, [0, m)h; h2 = h as mod special dual like number interval and [0, m)k, k2 = (m − 1) k as mod special quasi dual number interval. However there is only one real interval (∞, ∞) but there are infinitely many mod real intervals [0, m); 2 ≤ m ≤ ∞. The mod complex modulo finite integer interval (0, m) iF; iF2= (m − 1) does not satisfy any nice properly as that interval is not closed under product . Here we define mod transformations and discuss several interesting features about them. So chapter one of this book serves the purpose of only recalling these properties.
mod real interval, mod neutrosophic interval, neutrosophic logic
W.B. Vasantha Kandasamy, K. Ilanthenral, F. Smarandache. Multidimensional MOD Planes. Brussels: EuropaNova ASBL, 2015
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