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1 de oct. de 2020 · Your proof is correct, but a bit redundant. You showed that max(A) + max(B) ≥ x max (A) + max (B) ≥ x for all x ∈ A + B x ∈ A + B, and you explained how max(A) + max(B) ∈ A + B max (A) + max (B) ∈ A + B. This suffices to show what we need, as we've found an upper bound for A + B A + B that also belongs in A + B A + B, hence it's the ...
$\begingroup$ I prefer $\max\{f(x_1,\ldots,f(x_n)\}$ with curly braces and no parentheses. In this instance, the parentheses don't actually help, and the curly braces remind you that the thing whose maximum is sought is a set rather than a tuple. $\endgroup$
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
21 de ago. de 2011 · M (x) is a function. Taking the maximal number amongst the parameters. max {x1, x2} = {x1, if x1> x2 x2, otherwise. You can define like that the maximum of any finitely many elements. When the parameters are an infinite set of values, then it is implied that one of them is maximal (namely that there is a greatest one, unlike the set {− 1 n ...
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
11 de may. de 2020 · But let's take x = 2, then (1 - 2) ^ 2 will be (-1) ^2 which is nothing but 1 and according to op's max function, 1 should be returned. But since you gave the condition of x >= 1, we always return 0 even when x is something like 2. I think in comments what Andre Holzner said is correct.
A general result called Von Neumann-Fan minimax theorem states the following: Theorem 2 (Von Neumann-Fan minimax theorem). Let X and Y be Banach spaces.Let C ⊂ X be nonempty and convex, and let D ⊂ Y be nonempty, weakly compact and convex. Let g: X × Y → R be convex with respect to x ∈ C and concave and upper-semicontinuous with ...
19 de sept. de 2017 · Since composition of convex functions is convex, we only need to show max (x, y) is convex. But max (x, y) = x + y 2 + | x − y 2 | and | ⋅ | is obviously convex. A function f: Rn → R is convex if and only if its epigraph epif = {(x, t) ∈ Rn × R ∣ f(x) ≤ t} is a convex set.
Show that the $\max{ \{ x,y \} }= \dfrac{x+y+|x-y|}{2}$. I do not understand how to go about completing this problem or even where to start.
