2006-09-05 16:18:51 · 4 answers · asked by ttybrs10 1 in Science & Mathematics ➔ Mathematics
Incomplete question. If the hotel has the same number of rooms as there are positive integers, an additional infinite number of guests can be accomodated by sending the old guest in room n to room 2n and putting the new guests in the odd numbered rooms. There are many variants. If an infinite number of busses arrive every day with an infinite number of passengers and the hotel has to accomodate passengers for an infinite number of days, just send passenger k on bus m on day n to the hotel room numbered 2^k 3^m 5^n. There will still be infinitely many rooms open to accomodate more guests.
2006-09-05 16:27:43 · answer #1 · answered by mathematician 7 · 1⤊ 0⤋
There's that king of the paradoxes again - the word "infinite".
What would happen if the no vacancy sign were up and another guest arrived? How could you possibly explain to him that your infinite hotel was filled up?
2006-09-05 23:27:06 · answer #2 · answered by LeAnne 7 · 0⤊ 1⤋
I think the solution is undefined.
2006-09-06 21:58:44 · answer #3 · answered by Anonymous · 0⤊ 0⤋
The answer is pie. It always is...
2006-09-05 23:24:23 · answer #4 · answered by God 3 · 0⤊ 1⤋