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Aug 21, 2011 · $\max\{x_1,x_2\} = \cases{x_1, \text{if }x_1 > x_2\\x_2, \text{otherwise}}$ 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 $\{-\frac{1}{n} | n\in\mathbb{N}\}$ where there is no greatest element)
$\begingroup$ 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. $\endgroup$
$\begingroup$ I feel like allowing $\arg\max f(x)$ to be either $\in \mathbb{R}$ or $\in \mathcal{P}(\mathbb{R})$ is a very troublesome definition.
May 11, 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).
Feb 25, 2016 · max( max(a,c)+e) ) + max( max(b,d)+ f) (2nd application of result). max(a,c,e) + max(b,d,f) (associativity of max). max(a,c,e) + max(b,d,f) (associativity of max). This is the pattern for the general case, adding the n+1 term x+y
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Oct 1, 2020 · Suppose $\max(A)$ and $\max(B)$ exist, show that $\max(A+B)$ also exists and that $$\max(A+B)= \max(A) + \max(B)$$ I have the following proof I'm not sure if it's correct:
Nov 26, 2020 · Let X1 and X2 be two independent random variables both having discrete uniform distribution over 1, 2,.., n for some positive integer n.
Oct 16, 2015 · The space between "arg" and "min" is confusing; it would better be written "argmin". What the operator argmin does, when applied to a function, is pick out the point in the function's domain at which the function takes its minimum value (assuming that the point is unique).
