2 Jan
2012
2 Jan
'12
7:21 a.m.
* Dan Asimov <dasimov@earthlink.net> [Jan 01. 2012 17:16]:
Since high school I've thought factorial base is an interesting way to express real numbers in the unit interval (0,1).
That is, since 1/2! + 2/3! + 3/4! + ... = (d/dx((e^x-1)/x))(1) = 1, every x in (0,1) has a unique representation of the form
x = Sum_{n=1..oo} c_n/(n+1)!
if the integers c_n satisfy 0 <= c_n <= n.
I do not think so: 1/2 = 0.1 = sum( n>=2, n/(n+1)! ) The problem (same as 1.0 = 0.999.. ) stays with all mixed radix representations. For uniqueness I'd should check non-adjacent forms (no two adjacent digits nonzero), e.g., digits 0,+1,-1 in binary.
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