1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Number Theory (Finite and Infinite Sets)

  1. Nov 19, 2009 #1
    1. The problem statement, all variables and given/known data

    Why is R\Q not countably infinate or denumerable? Given R (Real Number) is not countably infinate or denumerable and Q (rational number) is denumerable.

    2. Relevant equations

    A set is said to be denumberable or countably infinate if there exists a bijestion of N (natural Number) onto S.

    3. The attempt at a solution

    Let Q be a subset of R and Let S be R-Q, which is denumerable. Via the defn there exists a bijection but R-Q is not bijective R-Q is the set of Real Numbers which is already not denumerable. I showed this to my prof and he said its not correct. He said to use Q u (R-Q)=R, we know Q is denumerable and R not to be denumerable use this to show R-Q is not denumerable? HOW!
     
  2. jcsd
  3. Nov 19, 2009 #2
    What you need to show is that the union of two countably infinite sets is countable. So take two sets {A_n} and {B_n}. Can you find a bijection from their union to the natural numbers? (hint: it's really easy)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Number Theory (Finite and Infinite Sets)
Loading...