Infinity is actually the truth and is what exists in reality.
What is missing in argument is four-fold:
1. Not realizing there are different sizes of infinities.
2. Not realizing two infinities of equal size can cancel out each other.
3. Not realizing it's possible to go past an infinity.
4. Changing definitions.
In the hotel experiment, if there are an infinite number of rooms and all rooms are filled with an infinite number of people, then with that definition, all rooms are canceled out.
This is because:
infinity - infinity = zero (assuming they are equal)
Infinity Hotels - Infinity People = Zero Rooms Left
However, if it were:
Infinity Hotels - Finite People = Infinity Rooms Left
Thus, right from the start, if all the rooms were filled, you cannot (by definition) add another person. This was the mistake, and doesn't discount there is an infinity - it's just matched with another, equal infinity canceling them all out.
However, once you define you are ABLE to add another person, you are redefining the infinity to be infinity + 1, but that "+1" is outside the original infinity (hotels) and incorporates a much larger one.
Yes, there are infinity hotels but it's match with an equally number of infinite people, this makes there (logically) to not have any rooms left.
To say "All" and then, "No, not 'all'" is the mistake and it just changes in definition. But the original argument assumes there cannot be infinities of greater or equal magnitude, but there can.
You can see my video here on how we can define infinities, which also relates to the subject. In it the cells can represent hotels and the people numbers:
https://m.youtube.co...h?v=oiCS9VnmPvw