Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof of Transcendentals Uncountable

  1. Sep 8, 2010 #1
    Hi guys,
    My question is to prove that the set of algebraic numbers is countable, then also prove that the set of transcendentals are uncountable. I have already proved the countability of the algebraics but now i do not know how to proceed. I beleive it could be as simple as the complement of the algebraics in R is uncountable, but I am not sure if the complement of the algebraics numbers within R is the set of transcendentals or not. I was unable to find out if this is the case.. I saw that trascendtals could possibly be complex, but in any case, if transcendentals make up the rest of R, then I would be done.. Any help would be great.. If anyone needs to see my proof of algebraics being countable I will post if someone asks.
  2. jcsd
  3. Sep 8, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Isn't a trascendental number by definition any number which is not algebraic?
    And that R - A is uncountable for any countable (or finite, of course) subset A is a general theorem.
    So I think you are done.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook