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Yes. This is explained in, among other places, the videos I linked to above. The most important is to recognise the difference between "countable" and "uncountable" infinity. The first is the size of the "counting" numbers 1,2,3... , while the second is the size of the number line -- ie, the answer to the question "How many numbers are there between zero and one?" The key concept is that "countable" infinities are those where you could conceivably count them off, one-by-one. Even though you never stopped, there would be some sense of making progress through the list.
It's possible to prove that one is literally bigger than the other by Cantor's diagonal argument, which should appear in two of the videos linked to above. It sort of runs like this, though:
1. Imagine you have a list of every number between zero and one.
2. This list is countable, by definition (because it's in a list form, so you can count off the entries).
3. On the other hand, you can easily construct a number that doesn't appear in the list, in the following way: change the first digit of the first number in the list by one, the second digit of the second number in the list by one, etc.
4. This new number is therefore different from every one of the numbers on the list.
5. You can always do this, so, no matter how many numbers there are on the list, you can always find at least one more that wasn't on it.
Therefore, there are more numbers between zero and one than can ever be listed, and the infinity is hence literally bigger than countable. The video probably explains it better, but in any case this is the sort of thing that requires a few run-throughs to appreciate, so please don't feel bad if you don't "get" it instantly.