Results 1 to 2 of 2

Math Help - Qestion in set theory

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    3

    Qestion in set theory

    L is the set of cofinite subsets of N (i'm not sure if i understand the concept of cofinite sets).
    I need to prove that L is countable. How do i prove this? What to do?

    Thanks for any kind of help :-)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,644
    Thanks
    1596
    Awards
    1
    Quote Originally Posted by John G View Post
    L is the set of cofinite subsets of N (i'm not sure if i understand the concept of cofinite sets). I need to prove that L is countable.

    I will assume that \mathbb{N} = \mathbb{Z}^ + the positive integers.
    A cofinite set has the property that its complement is finite.
    Thus each finite subset of \mathbb{N} corresponds to a cofinite subset of \mathbb{N}.
    The collection of finite subsets of \mathbb{N} is a countable set.
    Lets say that \mathbb{L} is collections of finite sets, define a mapping from \mathbb{L} to \mathbb{N} as follows.
    Make a listing of the prime numbers, \left\{ {p_1 ,p_2 ,p_3 ,p_4 , \cdots } \right\}.
    H: \mathbb{L} \mapsto \mathbb{N} by
    H(B) = \left\{ {\begin{array}{*{20}c}<br />
{1,} & {B = \emptyset } \\<br />
{\prod\limits_{x \in B} {p_x } } & {else} \\<br />
\end{array} } \right.
    Then show that H is injective.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Textbooks on Galois Theory and Algebraic Number Theory
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: July 8th 2011, 06:09 PM
  2. Group Theory - Sylow Theory and simple groups
    Posted in the Advanced Algebra Forum
    Replies: 16
    Last Post: May 16th 2009, 11:10 AM
  3. Set Theory
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: February 17th 2009, 02:08 PM
  4. Problems relating Theory of Automata (Computer Theory)
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: October 17th 2007, 09:52 AM
  5. 2 calculus qestion
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 29th 2007, 06:38 AM

Search Tags


/mathhelpforum @mathhelpforum