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May 17, 2013 at 5:29 vote accept andy teich
May 16, 2013 at 22:19 comment added George Lowther @andy: By definition of the supremum, for each n you can choose $d(P_n,P_1+\cdots+P_{n-1})$ as close as you like to the supremum, so can certainly choose it to be at least 1/2 of it.
May 16, 2013 at 22:12 comment added andy teich This is really beautiful!The only thing I have still to think about is the existence of such a sequence $(\mathbb P_n){n\in\mathbb N}$...
May 16, 2013 at 20:36 history answered George Lowther CC BY-SA 3.0