Basic Properties of Genetic Algorithm

We follow the rules: D is a non empty set, f1, f2 are finite sequences of elements of D, and i, n, n1, n2, n3, n4, n5, n6 are natural numbers. We now state two propositions: (1) If n ¬ len f1, then (f1 a f2)⇂n = ((f1)⇂n) a f2. (2) (f1 a f2)↾(len f1 + i) = f1 a (f2↾i). A Gene-Set is a non-empty non empty finite sequence. Let S be a Gene-Set. We introduce GA− SpaceS as a synonym of UnionS. Let f be a non-empty non empty function. Note that Union f is non empty. Let S be a Gene-Set. A finite sequence of elements of GA− SpaceS is said to be a Individual of S if: (Def. 1) len it = lenS and for every i such that i ∈ dom it holds it(i) ∈ S(i).