I am having trouble with the following terms: countably infinite, uncountable, and finite. In addition, for the following problems I need to select which category they fall into.
$1)$ Consider a set of every function from integers to the set ${false, true}$.
Would this be finite?
$2)$ Points in $4D$ (coordinates written as $(a,b,c,d))$;
This is uncountable, right?
$3)$ The set of functions from natural numbers to the reals that are within $O(n^2)$.
No idea where to start for this one.
Best Answer
The size of any set is obviously greater than or equal to the size of any subset. This gives us some inheritance relations:
For your problems: