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]

Ok I understand the concept of infinite countability and that say the set of all rational #s is infinitely countable

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.

, 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.

S = {x : x is rational}. Sometimes Q is used to represent rational numbers, so you could also say S = {x : x $\in$ Q}.

Also say I wanted to show a set of finite countable numbers, I'm sure I can just write T={1,2,3,4}

This is an example of a finite set. The way you wrote it, above, is fine.

but shouldn't i do something more proper and state that T = {n ε rat. # : 1≤n≤4}?

This would be all of the rational numbers between 1 and 4. This set is not the same as {1, 2, 3, 4}.

I just need help with how to properly represent sets- Thanks!