Results 1 to 2 of 2

Math Help - algebraic numbers

  1. #1
    Newbie
    Joined
    Feb 2011
    Posts
    3

    algebraic numbers

    How do I show that a set of algebraic numbers 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
    The algebraic numbers are the roots of polynomials with integer coefficients. A polynomial of degree n has at most n roots. There are countably many integers. The polynomials can easily be put into one to one correspondence with the set of finite sequences of integers which is countable. Now see if you can put all this together.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Algebraic Numbers
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: October 10th 2011, 02:54 PM
  2. algebraic numbers
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: July 28th 2011, 11:00 AM
  3. Algebraic numbers
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: October 13th 2010, 03:56 AM
  4. Proof: All rational numbers are algebraic numbers
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: September 5th 2010, 10:26 AM
  5. Algebraic Numbers
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 1st 2010, 09:21 AM

Search Tags


/mathhelpforum @mathhelpforum