Example 1.2.24: Let C be a set in n-dimensional space, and let Q(C) = ∫...∫Cdx1dx2...dxn. If C= {(x1,x2,...,xn : 0 ≤ x1 ≤ x2 ≤ ... ≤ xn ≤ 1}, then Q(C) = ∫01 ∫0xn∫0xn-1...∫0x3∫0x2dx1dx2...dxn = 1/n!. (Apologies for the poor formatting of the integration bounds.)
I haven't the foggiest idea how...
I am self-studying Boas and this is a problem from Ch. 1.2. I have developed what I believe is an answer, but I'm not sure it's adequate. The general approach is to show that for all values of n > 1, n^n grows faster than n!, and therefore that (n^n)/n! approaches infinity as n approaches...