infinite and finite countable sets

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!

Mark44

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.
[QUOTE=hatsu27;4175569]
, 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.
[quote]S = {x : x is rational}. Sometimes Q is used to represent rational numbers, so you could also say S = {x : x ##\in## Q}.
This is an example of a finite set. The way you wrote it, above, is fine.
This would be all of the rational numbers between 1 and 4. This set is not the same as {1, 2, 3, 4}.