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Oct 1, 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 ...
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) = 1 2(a + b + (− a + b)) = 1 2(a + b + | b − a |) = 1 2(a + b + | a − b |) Is this valid?
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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 ...
Sep 28, 2009 · Discussion Starter. Sep 28, 2009. #1. The max function is a function of 2 variables and is defined as follows: max (a,b) = {a if a > or = b. or {b if a < b. Express this piecewise defined function in one line using the absolute value function. We have never explored this max function before...not sure how to set this one up?
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Oct 19, 2016 · $\begingroup$ I've got the number max{a,b} and a,b∈R max{a,b}=a, a≥b or max{a,b}=b, a<b We can see that max{a,b}≤c only if a≤c and b≤c Now, if a,b,c,d ∈ R , prove that max{a+b,c+d} ≤ max{a,c} + max{b,d} I am really stuck here, I need this for my University. $\endgroup$ –
Jul 6, 2018 · 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.
Nov 30, 2021 · The easiest way to prove your equality is to split the two possible cases. In both cases, we will use the fact that multiplying an inequality by − 1 reverses the direction of the inequality, i.e. if x <y, then − x> − y. If a <b a <b. , then min (a, b) = a min (a, b) = a. , which means − min (a, b) = − a − min (a, b) = − a. Also ...
Oct 28, 2014 · 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.
