Suppose you have a hotel which has one floor with infinite number of rooms in a row and all of them are occupied. A new customer wants to check in, how will you accommodate her? What if infinite number of people want to check in, how will you accommodate them then?
Hint: Define infinity. :)
Update (18/12/09): Solution in comments by Nikhil Pandey (CSE, IITB alumnus)
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1) ask everyone to move to next room
ReplyDelete2) ask everyone to move from x>2x
????
pandeyji.. (@Gold and Iron)
ReplyDeletesahi jawaab.. dhanyawaad. :)
Since there are infinite number of rooms and infinite+1= infinite
Just ask person in room k to move to k+1. Thus making a room in the first room. :)
In the other case, since infinite+infinite = infinite
asking person in room k to move to 2k solves the problem.
Third part: Suppose infinite number of buses arrive at the hotel, each having infinite number of people, how will you accommodate them? :)
ReplyDelete@Sherminator..
ReplyDeleteNice one..
Since NxN is countable set. We can get a one to one mapping from N to NxN
Hence, we can accommodate (infinite people X infinite buses) in the hotel.
Relevant article:
http://en.wikipedia.org/wiki/Cantor_pairing_function
Thanks!
@Pratik . Infinite number of buses having infinite number of people would make the set N^N i.e. N x N x N..... N times...
ReplyDeleteInfinite Cartesian product of countable sets is uncountable
ReplyDeleteOh got it . Its a countable union of countable set.
ReplyDelete