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Infinite and finite countable sets

  1. Nov 27, 2012 #1
    Ok I understand the concept of infinite countability and that say the set of all rational #s is infinitely countable, but if I needed to represent the set how do I do that? S={xε rat. # : x= k , k ε a rational #}? that doesn't seem right. Also say I wanted to show a set of finite countable numbers, I'm sure I can just write T={1,2,3,4} but shouldn't i do something more proper and state that T = {n ε rat. # : 1≤n≤4}? I just need help with how to properly represent sets- Thanks!
  2. jcsd
  3. Nov 27, 2012 #2


    Staff: Mentor

    You are mixing up the terms. The positive integers and the rationals are countably infinite, and the reals are uncountably infinite. No set is described as being infinitely countable.
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