Collective Operations on Number-Membered Sets

The articles [4], [2], [1], and [3] provide the notation and terminology for this paper. For simplicity, we use the following convention: w, w1, w2 denote elements of R, c, c1, c2 denote elements of C, A, B, C, D denote complex-membered sets, F , G, H, I denote extended real-membered sets, a, b denote complex numbers, f , g denote extended real numbers, r denotes a real number, and e denotes a set. Let us consider w. Then −w is an element of R. Then w−1 is an element of R. Let us consider w1. Then w · w1 is an element of R. Let a, b, c, d be complex numbers. Note that {a, b, c, d} is complex-membered. Let a, b, c, d be extended real numbers. Observe that {a, b, c, d} is extended real-membered. Let F be an extended real-membered set. The functor F yielding an extended real-membered set is defined as follows: (Def. 1) F = {−w : w ∈ F}.