Introduction to Several Concepts of Convexity and Semicontinuity for Function from R to R
نویسندگان
چکیده
We adopt the following convention: a, b, r, s, x0, x are real numbers, f , g are partial functions from R to R, and X, Y are sets. The following propositions are true: (1) max(a, b) min(a, b). (2) Let n be a natural number, R1, R2 be elements of R , and r1, r2 be real numbers. Then R1 a 〈r1〉 • R2 a 〈r2〉 = (R1 • R2) a 〈r1 · r2〉. (3) Let n be a natural number and R be an element of R. Suppose ∑ R = 0 and for every natural number i such that i ∈ domR holds 0 ¬ R(i). Let i be a natural number. If i ∈ domR, then R(i) = 0.
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