Heavenly Problem III
So, if you haven't looked at the first two Heavenly Problem then please do so.
That way I don't have to repeat the components about Heaven Hotel.
So the spirit earns a room as the manager hotel solved it by telling every guest to move over 1 room. 1st room to 2nd room, 2nd room to 3rd room and so on.
And because there are infinite amount of rooms, the first room should be vacant so the spirit goes in there.
So all the spirits from the "Down below" came up and went to the back of the hotel and filled in.
Since there's infinite number of hotel rooms, there should be infinite number of vacant hotel rooms in the back (starting with room number infinity, infinity-1, infinity-2....and so on(?)).
But once again, there was that "No Vacancy" sign up on the front gate of Heaven Hotel.
And on Earth, there was a major volcanic eruption at the Ring of Fire and a major tsunami at the Paficific Ocean and a terrorist attack in India Subcontinent and USA.
So a lot of people died and came to Heaven Hotel.
The manager angel started putting the dead from the side door, starting with infinity/2, infinity/2 + 1, infinity/2 - 1, and so on(?), splittig the group to two sides.
But as the dead started to pile into Heaven Hotel,
the manager angel realised that finally the Heaven Hotel had truly No Vacancy.
How is this possible if there's an infinite nummer of rooms??
That way I don't have to repeat the components about Heaven Hotel.
So the spirit earns a room as the manager hotel solved it by telling every guest to move over 1 room. 1st room to 2nd room, 2nd room to 3rd room and so on.
And because there are infinite amount of rooms, the first room should be vacant so the spirit goes in there.
So all the spirits from the "Down below" came up and went to the back of the hotel and filled in.
Since there's infinite number of hotel rooms, there should be infinite number of vacant hotel rooms in the back (starting with room number infinity, infinity-1, infinity-2....and so on(?)).
But once again, there was that "No Vacancy" sign up on the front gate of Heaven Hotel.
And on Earth, there was a major volcanic eruption at the Ring of Fire and a major tsunami at the Paficific Ocean and a terrorist attack in India Subcontinent and USA.
So a lot of people died and came to Heaven Hotel.
The manager angel started putting the dead from the side door, starting with infinity/2, infinity/2 + 1, infinity/2 - 1, and so on(?), splittig the group to two sides.
But as the dead started to pile into Heaven Hotel,
the manager angel realised that finally the Heaven Hotel had truly No Vacancy.
How is this possible if there's an infinite nummer of rooms??
posted by James Yu at
7:42 PM
24 Comments:
Due to the number of spirits from Hell, the hotel will never finish finding them all room.
Otherwise we should have no problem finding all the new souls room. Consider that there are less than seven billion people in the world. Therefore we have afinite number of people, which is less than the second problem. So if we stop letting the people from hell, let the new people in, and then once they have rooms, let the infinite number of people from hell in, we can solve our problem pretty easily.
Personallt i'm still not convinced by the second answer, how does a spirit find the room infinity -1.
I am concerned about those coming from Hell. Are they coming to stay, or is it just a limited vacation? Are all coming, or just those who are not to dangerous? Hopefully those worst cases are not coming are they?
for heavenly problem II:
the spirits from hell wont be able to find infinty-x because they cannot find infinity. They will simply have to start at the front and keep walking until they find an available room (if they were nice, they could count the number of rooms for the manager)
for aj517's answer:
There is not a finite number of people on earth. Yes there are a finite number of people on earth AT THIS TIME but that number is always changing. The the seven billion people on earth right now will eventually die :( and be replaced by new people :)
I would recommend sending everyone back to hell and not mess with the order of the universe.
P.S. Why doesn't god fire that incompent manager. His only job is to keep count of the number of people in heaven. Being an angel and all, He should be able to do this; but noooooooo, this is just way to complicated for him. Maybe they should just get rid of him and invest in an electronic count keeper
I am also concerned for the workers in this hotel. How many housekeepers does it take to vaccum the rooms, to change the sheets, and fluff the pillows?
I would guess about 1/20 of infinity, so each must do 20 per day, and do they get health benefits?
With an infinite number of rroms, there will never be a situation where there is NO VACANCY!
The only issue is that check-in time may take an eternity before one is actually assigned a room.
As for the souls from hell, simply force them to find their own rooms and check-in those souls of the nearly departed.
Just make certain hotel security keeps the rudeness of the hellish souls from ejecting the heavenly souls from their assigned rooms.
WHY ARE YOU CRAZY PEOPLE DEBATING THIS ??? =| ITS NOT REAL!!!!!!!!!!!!! ... gosh!
It appears it happened because those from "down below" started filling in the rooms from the large "back end" of infinty (infinty, infinity-1, infinity-2, infinity-3...). While at the same time those souls from the disasters would be filling the rooms from the bottom-up. Eventually, given enough souls, the 'top-down souls' will overlap with the 'bottom-up souls' leaving more souls than rooms available.
Only problem is - there is no "back end" to infinity. The 'down bellow souls' could not have started from their first "room number infinty".
The best the manager can hope for - in the infinite - is to insure all rooms are equivelant and indistinguishable from one another, remove all the numbers from the doors, distroy his ledger, and remove the gates...Anything less would not be truely infinite. Would it?
Hottie, we know its not real, but it's realy fun to talk about.
Actually from a more philosphical perspective there will only ever be a finite of people full stop unless we assume the human race will never end - which might be problematic if the universe were to ever end. Either the overal solution should be this:
In the beginning there must have been a first human - all theories on origin at least agree on this - and so if we start counting from here and then keep going we have a way of counting and thus assigning rooms. So the a new inifinite hotel should be built in which a room assigned by date of birth. Now if a soul accepts his room, give to him, but if a soul does not - for example he is in hell, then leave a room empty, now move everyone from the first hotel to the new one by offering a complementary glass of champagne in each room. Now we will have a room for everyone. Hazzar, and we are done.
You should not begin counting rooms from "infinity" backwards. It does not work that way. You should not start at infinty as if it were a real number. Doing so releases great demons unto the world...
The way I see it, all the hell hounds and disaster victims are being assigned to one sigle room.
Since infinity minus x is still infinity and infinity/2-x is still infinity, they are all being put into room# infinity.
It doesn't matter if the room is big enough to hold them all, as they will never find it anyway.
oh.. and the manager angle is on crack, because there's still an infinite number of rooms available..
Infinity is not a real number, nor is it finite. So dividing infinite by any number is impossible. And since you cannote divide by infinity, you cannot get infinity/2 because it would have to be a variable. Since the # would vary, adding 1 or subtracting 1 means it changes
^i'm the same person as that the anonymous above, and i forgot 2 answer the question. Its impossible since u can't reach the back room, since there is infinitely many rooms that cannot be in the back. Since it goes on forever, you cannot reach the back.
However, if they did find a finite room, then they would fill in the rooms inbetween, like so
F<<<<<<<<<<<<<<<__>>>>>>>>>>>>>>>>B
F is the Front
B is the Back
The underscore represents the middle and the arrows represents them moving out to fill it in.
Your all idiots. There is no problem here, its merely a stupid question.
The number of people that have ever lived is just over 100 billion. Whenever the inept innkeeper loses count, simply start a new ledger at some number larger than 100B (adjusted for the number of people born during the time he does remember).
Can inept innkeepers in heaven be punished? Can the inept innkeeper simply ask the all-knowing which rooms have not been filled?
Alternatively, the housekeepers can tell the inept innkeeper which rooms are available.
Do the housekeepers get special heaven privileges? Or are they second-class angels? Is it allowed to complain about their work?
Finally, the souls trying to find room infinity minus n will be searching forever, and hence will never occupy a room.
how can there even be a room number 1nfinity, infinity-1, or infinity/2, etc. Infinity isn't a number, and if you look for a room number infinity or infinity -1, you will never find it. So (like steve said) why doesn't he just ask "the all-knowing" what the vacant room numbers are.
Also, what does infinity/2 or infinity-1 even equal?
Or pick a large random room number. The odds that they'll come back and complain because his room is occupied is close to nil, since 1/gazillion ~= 0. That's much less chance than the innkeeper forgetting which rooms are occupied, apparently. Besides, the innkeeper clearly needs some time off to enjoy his stay. Just post a sign "pick a huge random number and go to that room".
simple... there isnt such thing as heaven thus there are infact no rooms available as such
Ok so I'll go the logic route. It has to do with limits. Infinity is used quite often with respect to limits. And inf-x < inf; therefore the answer to the first heaven prob makes sense. The answer for the second heaven prob again makes sense since you are starting at the opposite end. Consequently when multiple disasters occur sending another batch of souls to the hotel, it only makes sense to start in the middle somewhere. And if you take any number and divide it by 2 an infinite number of times it will eventually become zero. Effectively leaving no rooms available.
Or think of it in terms of distance... you can divide the distance between two objects in half...then divide the remaining distance in half...this can be done indefinitely...but at some point the two objects touch...this is possible because of limits.
Its a mathematical law from Differential Equations but I dont remember the name.
When you divide any number larger than 3 by 2, you'll indeed generate a room number, but you'll also skip at least one room, leaving that room (those rooms) vacant. Therefore you still have vacancies, although our inept innkeeper may be hard pressed to keep track of them.
Take the spirits from hell and move each of them down one room, since infinity>infinity-1, and since there are infinity rooms, room number infinity is the last room, so because infinity is a constantly increasing value, one less mus also rise. If the second-to-last room is referred to as a number, the chances of any random whole number not equaling infinity are infinity-1, which is a constantly increasing value, because if it weren't, it wouldn't equal infinity-1, so infinity-1 is a constantly increasing value, which I said was what infinity was. Anyway, the spirit in room number infinity is in the last room, so if the rooms are numbered in relation to infinity, there is no solution. You'd think souls would have their own houses in Heaven, anyway, which would also make things a lot easier. Damn, that was a lot of thinking for a kid. I might have used 11% of my brain's potential there! Btw, it is believed that we only use 10% of our brains' potential.
The reason there is no vacancy is because with all these new souls in the heaven hotel the manager is royally screwed and has even less of a clue how many souls there are and is thus forced to once again claim false no vacancy on the infinite roomed hotel.
This is the same anonymous person who posted March 31. The simple answer: convert to whatever doesn't involve Heaven
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