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$\begingroup$ 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. $\endgroup$
14. I am tasked with showing that. If a, b ∈R, show that max{a, b} = 1 2(a + b +|a − b|) I think I can say "without loss of generality, let a <b." Then b − a> 0 But also, max{a, b} = b = 1 2a + 1 2b − 1 2a + 1 2b. = 1 2(a + b − a + b)
Aug 21, 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 ...
$\begingroup$ 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.
Get the range of the required distribution, in this case, max(X, Y) Find the CDF of this distribution as a function of the known distributions Find the PDF of the distribution by differentiating the CDF
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.
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Sep 19, 2017 · One line proof: 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.
Jun 19, 2012 · Referring to this lecture , I want to know what is the difference between supremum and maximum. It looks same as far as the lecture is concerned when it explains pointwise supremum and pointwise ma...
Aug 12, 2018 · The maximum of a totally ordered set is defined as an element that is greater than all the other elements. For example max(4, 9] = 9 max (4, 9] = 9 since 9 9 is in (4, 9] (4, 9] and is greater than all the other elements. On the other hand, max(4, 9) max (4, 9) does not exist.
