If you're responding to the part about countable infinity and uncountable infinity, it's a bit of a misnomer, but it is the proper term.

Countably infinite is when you can pick any number in the set and know what comes next.

Uncountably infinite is when it's physically impossible to do that, such as with a set of all irrational numbers. You can pick any number you want, but it's impossible to count what came before or after it because you could just make the decimal even more precise, infinitely.

The bizarre thing about this property is that even if you paired every number in a uncountably infinite set (such as a set of all irrational numbers) with a countably infinite set (such as a set of all natural numbers) then no matter how you paired them, you would always find a number from the uncountably infinite set you forgot. Infinitely many in fact.

It's often demonstrated by drawing up a chart of all rational numbers, and pairing each with an irrational number. Even if you did it perfectly, you could change the first digit of the irrational number paired with one, change the second digit of the irrational number paired with two, and so on. Once you were done, you'd put all the new digits together in order, and now you have a new number that appears nowhere on your infinite list.
It'll be at least one digit off from every single number you have, because you just went through and changed those digits.

Because of that property, uncountably infinite sets are often said to be larger than countably infinite sets. I suppose depending on your definition that's true, but I think of it as just a different type of infinity.