My Math Forum Conjecture: Decimal Representation of root

 Number Theory Number Theory Math Forum

 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
Member

Joined: Sep 2010

Posts: 63
Thanks: 0

Re: Conjecture: Decimal Representation of root

Quote:
 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

### conjecture decimals definition

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post MrAwojobi Number Theory 66 June 2nd, 2014 07:59 AM blackers1778 Elementary Math 2 March 23rd, 2014 11:42 PM miket Number Theory 5 May 15th, 2013 05:35 PM enchev_eg Number Theory 30 September 28th, 2010 08:43 PM demipaul Linear Algebra 2 November 19th, 2009 05:42 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top