Paul
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 Sep24 awarded Autobiographer Jun12 comment efficient way to invert a Matrix plus a diagonal one This might lead nowhere, but is a bit like evaluating 1/(1+x). What happens if you expand in a Taylor series? Jun7 comment Prove that $f(x)=O(x)$ as $x\to 0$ True. As another example, if f(x) = sqrt(x) and a[n]=1/n^2, then f is not O(x) as x->0 and can be seen to transform the convergent series to a divergent one. Jun6 comment Prove that $f(x)=O(x)$ as $x\to 0$ Suppose that f(x) = c + g(x) s.t. g(x)->0 as x->0 and c>0. What happens to the sum? Jan19 comment Splitting a sandwich and not feeling deceived @Mars Perhaps that is not coincidental, as I once took something like 'Philosophy of Ethics' as an undergrad -- though I wasn't consciously thinking of it. Jan15 comment Splitting a sandwich and not feeling deceived @in_wolfram_we_trust Ah, but that collusion is not subgame perfect. Or, in less technical terms, you need an enforcement mechanism in case there is no honor among thieves. The cutter does have a knife :-) Also, it can be a repeated game. Or, there can be things that can happen externally. But if the cutter can't trust the person who gets the big piece, then there is no way to collude. Jan14 comment Splitting a sandwich and not feeling deceived Collusion, though possible, would not be subgame perfect. There are N people. I cut the sandwich into a large piece and N-1 tiny pieces, thinking that the recipient of the large piece will tip me a portion > (1/N). Problem is, they now have their meal, and they don't have to share. Such a bargain could only be enforced because (a) I have a knife, or (b) there is a repeated context, or (c) some other enforcement mechanism outside the game Jan14 comment Splitting a sandwich and not feeling deceived This seems trivial. Each person rolls dice. The low score cuts the sandwhich into portions. Then each participant chooses a single portion according to highest dice order. Now since the cutter chooses last, he will obtain the smallest portion, as in the case with 2 participants, but it is clear that the number of participants do not matter. Therefore, he will maximize the size of the smallest portion. But this must mean that all portions are equal. Am I missing something here? Jun13 awarded Supporter