Convergence Question (just for fun)
From: Tim Brauch (RnEeMwOs.pVoEst_at_tbrauch.cNOoSPAMm)
Date: 11/29/04
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Date: Mon, 29 Nov 2004 04:41:07 GMT
I was doing some work the other day, and had to keep taking the ceiling of
half of a value. Eventually, I found that I was taking the ceiling of half
of the ceiling of half of a value. And so on.
This led me to think about the following sequence of functions, and whether
it converges or not.
f_1(x) = ceil(x/2)
f_2(x) = ceil(ceil(x/2)/2) = ceil(f_1(x)/2)
f_3(x) = ceil(ceil(ceil(x/2)/2)/2) = ceil(ceil(f_1(x)/2)) = ceil(f_2(x)/2)
...
f_n(x) = ceil(f_n-1(x)/2)
...
It is not quite the same as
g_n(x) = x/(2^n)
I was just wondering if it converged.
- Tim
-- Timothy M. Brauch NSF Fellow Department of Mathematics University of Louisville email is: news (dot) post (at) tbrauch (dot) com
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