Re: [math-fun] Little number theory puzzle
Mike Stay inquires: << How do you select two integers independently at random? To pick one integer at random, just consider a dense subgroup of the circle C = R/Z -- say G = {n*sqrt(2) mod 1 : n is in Z} -- and consider the cosets C/G. Let W be a subset of C containing exactly one representative of each coset. Then C is the disjoint union of the countably many translates of W of the form T_k = k + W, for k in Z. Finally, pick a point at random from C. It belongs to exactly one T_k, and then k is your random integer. Pick another point independently from C in the same way to get two independent random integers. --Dan
Umm, this is a joke, right? Franklin T. Adams-Watters -----Original Message----- From: dasimov@earthlink.net Mike Stay inquires: << How do you select two integers independently at random? To pick one integer at random, just consider a dense subgroup of the circle C = R/Z -- say G = {n*sqrt(2) mod 1 : n is in Z} -- and consider the cosets C/G. Let W be a subset of C containing exactly one representative of each coset. Then C is the disjoint union of the countably many translates of W of the form T_k = k + W, for k in Z. Finally, pick a point at random from C. It belongs to exactly one T_k, and then k is your random integer. Pick another point independently from C in the same way to get two independent random integers. --Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun ___________________________________________________ Try the New Netscape Mail Today! Virtually Spam-Free | More Storage | Import Your Contact List http://mail.netscape.com
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