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Doing some homework I came across this notation:

$$ \max_{i=1}^n |x_i − c|$$

I have been given $n$ values of $x$. I need to perform a $\min$ function on this function for $c$ (might need help with that later) but for now can anyone explain what this "max summation" (at least thats what it looks like to me) function notation does? i.e. how would I write it out for $n=2$ and $x_i= 3 , 6$

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This notation is just another way of writing

$$ \max_{i} |x_i - c| $$

or even better

$$\max \{ |x_i - c| : i = 1, 2, \ldots , n \}. $$

It tells you to extract that maximum of that expression, running over all indices $i$.

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  • $\begingroup$ So I will find a different $c$ for every $i$ and then sum them all? Wouldn't my $c$ be infinite every time? also if I say $$f(x)=\max_{i=1}^n |x_i − c|$$ then what how do I find $$min(f(x))$$ $\endgroup$ Commented Nov 4, 2016 at 0:14
  • $\begingroup$ There is no summing involved. $\endgroup$ Commented Nov 4, 2016 at 1:00

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