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Homework Help: Countable, uncountable sets

  1. Sep 9, 2010 #1
    1. The problem statement, all variables and given/known data

    A complex number z is said to be algebraic if there are integers
    a0; a1...; an not all zero such that z is a root of the polynomial,
    Prove that the set of all algebraic numbers is countable.

    2. Relevant equations

    3. The attempt at a solution

    For every natural number N there are only finitely many such polynomials

    But how to prove the set is countable
  2. jcsd
  3. Sep 9, 2010 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    Finitely many such polynomials that do what?
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