Results 1 to 3 of 3

Thread: polynomials

  1. #1
    Newbie
    Joined
    Feb 2011
    Posts
    3

    polynomials

    how do I show that the set of polynomials with interger coefficients is countable?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2010
    From
    Staten Island, NY
    Posts
    451
    Thanks
    2
    See my response to your similar question about the algebraic numbers. If you're still stuck, say where you're stuck and I'll help you with the details.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    22
    Quote Originally Posted by ricky View Post
    how do I show that the set of polynomials with interger coefficients is countable?
    The set of all such polynomials of degree less than or equal to n, denoted by \mathbb{Z}_n[x] is clearly countable via the obvious identification \displaystyle f:\mathbb{Z}_n[x]\to\mathbb{Z}^{n+1}:\sum_{k=0}^{n}\alpha_k x^k\mapsto (\alpha_0,\cdots,\alpha_k). Note then that \displaystyle \mathbb{Z}[x]=\bigcup_{n\in\mathbb{N}}\mathbb{Z}_n[x] and so..
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: Apr 7th 2011, 01:38 PM
  2. GCD of polynomials in Zn[x]
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: May 18th 2010, 07:22 AM
  3. Polynomials
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 16th 2010, 07:52 AM
  4. Replies: 7
    Last Post: Jan 8th 2010, 04:13 AM
  5. Replies: 5
    Last Post: Nov 29th 2005, 04:22 PM

Search Tags


/mathhelpforum @mathhelpforum