Oh, in that case replace 11^n with: 10^n * (p_0 * p_1 * ... * p_n) / Q where each p_i is greater than 1 but the infinite product: p_0 * p_1 * p_2 * p_3 * ... converges to the finite value Q.
Sent: Saturday, September 12, 2015 at 12:24 PM From: "James Propp" <jamespropp@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Cantor set of measure 1?
I meant to add "and preserves the natural product measure on the set".
Jim Propp
On Saturday, September 12, 2015, Adam P. Goucher <apgoucher@gmx.com> wrote:
What's the nicest way to picture the product set S=DxDxDx... with D={0,1,2,...,8,9} as a subset of the reals so that lexicographic ordering of S is a restriction of the usual ordering of the reals?
f : (D x D x D x ...) --> R (d_0, d_1, d_2, ...) |--> sum(d_n / 11^n : n in {0, 1, 2, ...})
has the property you describe, unless I'm missing something.
Sincerely,
Adam P. Goucher
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