Quote Originally Posted by Savy View Post
Basically if something is countable you can essentially take every element in the set and say it's the same as 1, 2, 3 etc. The link I posted shows how you can do this for rational numbers.

There are some sets where if you do this it's impossible to have every element in that set match up to 1, 2, 3 etc. There is essentially stuff left over. It's why there are infinitely more numbers between 0 and 1 than there are natural numbers.
Is it fair to say it's one of those cases where the technical term simply means something else than the colloquial? Just because the R infinity isn't listable using the N infinity doesn't make the N one countable.