“…means to split C into three parts (two parts opposite to each other, and another part which is the neutral / indeterminacy between the opposites), as pertinent to neutrosophy {(< A >, < neutA >, < antiA >), or with other notation (T, I, F )}, meaning cases where C is partially true (T ), partially indeterminate (I), and partially false (F ). While anti-sophication of C means to totally deny C (meaning that C is made false on its whole domain) (for detail see Smarandache [21,22,24,25]). Neutro-sophication of an axiom on a given set X, means to split the set X into three regions such that: on one region the axiom is true (we say degree of truth T of the axiom), on another region the axiom is indeterminate (we say degree of indeterminacy I of the axiom), and on the third region the axiom is false (we say degree of falsehood F of the axiom), such that the union of the regions covers the whole set, while the regions may or may not be disjoint, where (T, I, F ) is different from (1, 0, 0) and from (0, 0, 1).…”