well the problem with infinity is that we cannot precive it.
example there is no number infinity because you can always add one so technically the argument that he had a full hotel with infinite number of rooms cannot be ever full because you can always add one.
our minds do not work that way they work infinity = infinity and we use the same logic as 100 = 100 so if you have 100 guests and 100 rooms the hotel is full. But if you have an infinite number of guests and an infinite number of rooms that does not mean that every room is full because there is no finite number of rooms you can always ad one and if a new geust shows up you added one guest and one room
so infinity +1 is still infinity
infinity is an imaginary number never obtainable because you can always ad one
As for the universe if it is infinitively large we do not know and we never will know if it is infinite we may one day know if it is finite.
™ Version 4.2
