Hilbert's paradox of the Grand Hotel - An easier solution?

[Office_Shredder]

I'm not saying that.. I'm saying the digit 1 with infinitely many zeroes before it can be read as a binary number that you can map to room number 1. The digits 11 with infinitely many zeroes before it can be read as a binary number that you can map to room number 3.. And so on. You have already answered yes to the question, when I asked if these combinations would occur in the list. Thats why I said that if you mirror the list, so it reads from right to left, then it's possible to map the passengers to their rooms.

I think most conceptions of an infinite string of 1s and 0s does not have any such thing as infinite 0s, and then a 1. There are actual interesting ways to think about ordering in which you could imagine the set of all strings of infinitely digits and then one extra digit, but the canonical representation there is no "last digit".

 

[Lars Krogh-Stea]

I think most conceptions of an infinite string of 1s and 0s does not have any such thing as infinite 0s, and then a 1. There are actual interesting ways to think about ordering in which you could imagine the set of all strings of infinitely digits and then one extra digit, but the canonical representation there is no "last digit".

I agree, but there is a first number. That's why I say "mirror the list".

Example: 100...0 will turn into 0...001. And for this practical application of mapping people to rooms, I see that as sufficient data to get the job done.

 

[Lars Krogh-Stea]

You're still trying to interpret the stings of ones and zeros as binary numbers. They are not. They are instances of members of a set. There is a mathematical study of boolean logic where such thoughts apply, but it is not relevant here.

If it works, it should be relevant..

 

[Mark44]

Example: 100...0 will turn into 0...001.

Bad example. Where is 100...0 on the number line?
And why not write the latter as just plain 1?

I think we've beaten this horse to death, so I'm closing this thread.