184 Are the Androids Dreaming Yet?

184 Are the Androids Dreaming Yet? Hunter with Spears Provided there are an infinite number of hunters there is always someone to hand the spear to and the person at the front of the line now has space for another spear. You can probably see how to answer Dermot’s question. The hotel manager calls the guest in the first room and asks him to move 3 rooms up rather than one. He then calls the remaining guests and tells them the same thing. Thus, he has managed to fit three more people into the infinite hotel. Infinity plus 3 is infinity. You may worry that it takes the manager an infinite time to call all the rooms, but it’s OK; he lives infinitely long so it all works out. What about fitting an infinite number of new guests into the already full hotel? Surely then we will get stuck. No, Hilbert’s Hotel can fit an infinite number of extra guests. Here’s the trick: ask all the people currently in the hotel to move to the room with double the number they are currently in — 1 goes to 2, 2 goes to 4, 3 goes to 6, and so on. Now all the odd numbers are empty and you can fit an infinite number of people into the empty odd rooms. Infinity plus infinity is infinity. Voila. HOUSE_OVERSIGHT_015874