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Radrook said:Adding guests doesn’t affect the hotel’s infinity in any way.
But if we add a room, or height, then the hotel wasn’t infinite to begin with because we cannot add to what is literally infinite. Perhaps you are confusing sequential infinity with literal infinity. They are completely different from each other.
Sequential infinity is represented by a number line with two arrows indicating that the number sequences go on forever. In short, that we can always add one more to the sequence.
Literal infinity doesn’t allow that. The fellow who wrote the article is confusing the two as well. In fact, he contradicts himself semantically by saying that a hotel’s infinite number of rooms are countable. Countability requires finiteness.
I don't know enough math to argue with you, but that doesn't seem right and consider that that a huge number of physicists seem to have no trouble with the idea that our universe may be infinite and I'm sure they are all aware that it is expanding. How do you explain that? What am I missing?