Results 1 to 3 of 3

Math Help - Interval Countability proof

  1. #1
    Member
    Joined
    Nov 2010
    Posts
    86

    Interval Countability proof

    Every interval [x,y] is uncountable.

    How to prove this? Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by jstarks44444 View Post
    Every interval [x,y] is uncountable.
    How to prove this?
    Without knowing what theorems go before this question, there is no way to give you an answer. For example: if a<b then the interval [a,b] is uncountable.
    The rational numbers are countable.
    So what does mean about [a,b]\setminus \mathbb{Q}~?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2010
    Posts
    86
    Ah, you're right. The theorems that come before this include,

    R (Reals) is not countable.
    The set R - Q (Rationals) of irrational numbers is uncountable.
    The set of transcendental numbers is uncountable.

    The proof of the reals not being countable shows that the set of decimals

    {0.d1d2d3...: each dj = 3 or 4} which is a subset of R

    is uncountable. Consequently, the interval [0,1] = {x in R : 0 <= x <= 1} is uncountable. This can apparently be modified to prove the theorem in question. Thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Countability of Subsets proof
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: December 10th 2010, 07:19 AM
  2. Countability proof.
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: November 29th 2010, 09:14 AM
  3. Countability of the interval (x,y) where x,y are in R
    Posted in the Differential Geometry Forum
    Replies: 8
    Last Post: September 7th 2009, 05:00 PM
  4. Countability Proof
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: January 21st 2009, 08:56 AM
  5. Proof of countability
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: February 15th 2007, 07:35 PM

Search Tags


/mathhelpforum @mathhelpforum