# Infinite and finite countable sets

1. Nov 27, 2012

### hatsu27

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. Nov 27, 2012

### 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.