September 27th, 2010, 01:56 PM  #1 
Member Joined: Sep 2010 Posts: 60 Thanks: 0  Cardinality of P I would really appreciate if you could help me! 
September 27th, 2010, 02:16 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Cardinality of P
I can't make sense of your notation.

September 27th, 2010, 02:19 PM  #3  
Global Moderator Joined: May 2007 Posts: 6,378 Thanks: 542  Re: Cardinality of P Quote:
 
September 27th, 2010, 02:22 PM  #4 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Cardinality of P
It's somewhere between N and R, probably closer to R... 
September 28th, 2010, 09:07 AM  #5 
Member Joined: Sep 2010 Posts: 60 Thanks: 0  Re: Cardinality of P
To tell the truth I don't really understand it, either. But I think: P is a set of polynomials n+1 is a set, because every natural number can be considered as a set k is element of n+1 a_k is an integer I really hope that the problem is clearer for you than for me... Any help would be appreciated. 
September 28th, 2010, 09:18 AM  #6 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Cardinality of P
OK, so . Good, that wasn't obvious to me. What is n? A fixed, unknown natural number? What coding do you use for natural numbers (or whatever sort of object n is)? We need to know since you want to money with the elements of a number, and numbers aren't usually thought of as having elements. Perhaps this means k in {0, ..., n} or k in {1, ..., n} as it would with two popular encodings. 
September 28th, 2010, 10:08 AM  #7  
Member Joined: Sep 2010 Posts: 60 Thanks: 0  Re: Cardinality of P Quote:
And you are right again, I suppose that it means that k is in {0,....,n} ( We definied natural numbers as sets, and the elements of n natural numbers are 0, 1, 2,....,n1) Sorry that my notation was confusing, but to tell the truth in the begining I can't understand this notation, either. But then I glanced through my notes and it cleard up a little bit. Unfortunatelly I can't solve the task yet anyway it has been already useful. I hope you can help me. I would really appreciate it. Thanks.  
September 28th, 2010, 10:18 AM  #8 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Cardinality of P
So you're trying to count the degreen polynomials with integer coefficients. That's , which is just .

September 29th, 2010, 01:54 AM  #9  
Member Joined: Sep 2010 Posts: 60 Thanks: 0  Re: Cardinality of P Quote:
 

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