Quote Originally Posted by ImSavy View Post

As the real numbers are uncountable, that makes them a bigger set. Therefore there is no amount of natural numbers we can use to match up them all, as we could always find a real number in between ANY two real numbers, whereas we can not find a natural number in between ANY two real numbers because natural numbers next to each other, i.e. 1&2, 8&9, 214124&214125 don't have another natural number between them.
The bold part, no amount of natural numbers is correct, but an infinite amount, well now we can.