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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(xiwi)+(wixi)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 welldefined; consider q1 = q2 = 1, r1 = 2, r2 = 2, N1 = N2 = 3. 
March 14th, 2011, 10:03 AM  #3  
Member Joined: Sep 2010 Posts: 63 Thanks: 0  Re: Conjecture: Decimal Representation of root Quote:
 

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