Originally posted by Vornskr:
"infinity + 1 > infinity" is an expression that doesn't make sense, because infinity isn't a number that you can perform ordinary operations with.
Like I said in my post above, the trouble is in trying to think about the number of rooms you have vs. the number of guests you have.
Instead, tell me this: under my proposed solution, is there ever a guest who doesn't get a room? Not guest #999, because he can move into room #1000. Not guest #999999, because he can move into room #1000000, and so on. No guest will ever have a problem here, because there's no "last guest" or "last room".
(I shouldn't do this, but to answer your question on your terms--remember that a mathematician would say they don't make sense--: you are right that "infinity + 1 > infinity" is false. In fact, to the extent that it makes sense, infinity + 1 = infinity. But that also shows us that the hotel won't have a problem. It had infinity rooms, so it could accommodate infinity guests. Then it got one more guest, so it had infinity + 1 guests, which is really just infinity guests. So the number of guests it has hasn't changed. So it can still fit everyone, including the new guest.
See why talking about it in these terms is eschewed by mathematicians?)
Like I said in my post above, the trouble is in trying to think about the number of rooms you have vs. the number of guests you have.
Instead, tell me this: under my proposed solution, is there ever a guest who doesn't get a room? Not guest #999, because he can move into room #1000. Not guest #999999, because he can move into room #1000000, and so on. No guest will ever have a problem here, because there's no "last guest" or "last room".
(I shouldn't do this, but to answer your question on your terms--remember that a mathematician would say they don't make sense--: you are right that "infinity + 1 > infinity" is false. In fact, to the extent that it makes sense, infinity + 1 = infinity. But that also shows us that the hotel won't have a problem. It had infinity rooms, so it could accommodate infinity guests. Then it got one more guest, so it had infinity + 1 guests, which is really just infinity guests. So the number of guests it has hasn't changed. So it can still fit everyone, including the new guest.
See why talking about it in these terms is eschewed by mathematicians?)
The last bit makes sense I guess. Thanks for explaining.
