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 March 11th, 2011, 10:45 AM #1 Member   Joined: Sep 2010 Posts: 63 Thanks: 0 Conjecture: Decimal Representation of root The Conjecture - Treat Each digit as a coordinate in a vector - Consider the space of numbers of the form w=q1*r1^(1/N1)+…+ qv*rv^(1/Nv) Where q is rational, N is an integer and no factors of r have an Nth root. -denote the digits of w as w0w1…wm And the inner product between two number w and x as: Lim (m->inf)(1/(2m))sum_1..m (wi(xi-wi)+(wi-xi)wi) Then if r1..rv and N1..Nv are known then qi is the projection of w on ri^(1/Ni) The rational Since irational numbers are random one expects their components to be orthogonal. I'm sure their are simple tests one could try to verify this. I will think of some later. March 11th, 2011, 11:54 AM #2 Global Moderator   Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Conjecture: Decimal Representation of root wi isn't well-defined; consider q1 = q2 = 1, r1 = 2, r2 = -2, N1 = N2 = 3.  March 14th, 2011, 10:03 AM   #3
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Re: Conjecture: Decimal Representation of root

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 Originally Posted by CRGreathouse wi isn't well-defined; consider q1 = q2 = 1, r1 = 2, r2 = -2, N1 = N2 = 3. opps. My miskate. r1 and r2 should be whole numbers. Anyway, I'll try to test it soon but I wish to make another post first. Tags conjecture, decimal, representation, root Search tags for this page

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