Abstract: The terminology and notation used in this paper have been introduced in the following articles: [23], [11], [1], [5], [6], [12], [9], [4], [24], [18], [19], [8], [7], [2], [20], [16], [13], [15], [14], [21], [22], [17], and [10]. We follow a convention: a, b, x, y, z denote real numbers and k, n denote natural numbers. We now state several propositions: (1) For every subspace A of the metric space of real numbers and for all points p, q of A and for all x, y such that x = p and y = q holds ρ(p, q) = |x− y|. (2) If x ≤ y and y ≤ z, then [x, y] ∪ [y, z] = [x, z]. (3) If x ≥ 0 and a+ x ≤ b, then a ≤ b. (4) If x ≥ 0 and a− x ≥ b, then a ≥ b. (5) If x > 0, then x > 0. In the sequel s1 will be a sequence of real numbers. Next we state the proposition (6) If s1 is increasing and rng s1 ⊆ , then n ≤ s1(n). Let us consider s1, k. The functor k s1 yielding a sequence of real numbers is defined by: (Def.1) for every n holds k1(n) = ks1(n).
Publication Year: 1991
Publication Date: 1991-01-01
Language: en
Type: article
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Cited By Count: 1
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