A countable infinity is a infinity you can count. An example would be how many hours are in infinity.

On a number line, you would right it as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, . . .

Even though it goes on forever, it is still countable.

Now, we shall go onto uncountable infinity. If we put it on a number line it would be even BIGGER! These numbers would be called the real numbers.

EX: The numbers between 0 and 1. I mean, where do you start. All you know is that it would be a number with ongoing zeros then end with a 1. Like 0.000000000000000 . . . 1. This would be countable.