- #1

dakiprae

- 15

- 0

- TL;DR Summary
- Hilbert's Hotel often shown as a veridical Paradox. I want to show my argument, why the argument 'every guest n moves into the next room n+1' is not provable true.

Hello there,

I had another similar post, where asking for proof for Hilbert’s Hotel.

After rethinking this topic, I want to show you a new example. It tries to show why that the sentence, every guest moves into the next room, hides the fact, that we don’t understand what will happen in this infinite thought experiment (mathematically and logically).

If you don't know Hilbert's Hotel you can read it on Wikipedia:

https://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel

Wikipedia article of Hilberts Hotel captor Analysis:

Hilbert's paradox is a veridical paradox: it leads to a counter-intuitive result that is provably true.

My argument, why I think it is not provable true:

First I want to explain my own example (A), than we go back to Hilbert's Hotel (B): Guest 1 moves out and knocks on Guest 2’s door. Guest 2 goes out. Guest 1 moves in the Room 2 and Guest 2 knocks on Guest 3’s door. Repeat this process every second. If you repeat this forever, there is always one guest n outside knocking on n+1's door. Here we have potential infinity, but never reach infinity. But after an infinite amount of time, every single guest moved. Finally, every guest n has moved in n + 1 Room. No more guest is outside anymore, because all moved. Something happens, which used to be impossible before.

Back to Hilbert's Hotel (B): The mathematical or logical argument for Hilbert's Hotel Paradox is: Every guest can move to n + 1 room. So you can make room for any new guest (Peano axioms).

I would say, there is no logical or mathematical proof, that every single guest will move into the next room in this thought experiment. It's not clear what will happen in this infinity scenario. If you go with my argument, Hilbert’s Hotel is an unsolved topic and not a veridical paradox. Saying every guest moves into the next room in Hilbert's Hotel is like saying every guest moves into the next room in my example (A) above. I am not sure, if every guest moves into the next room, because I don't know how this infinite sets interact with each other. If we don't know how this two infinite sets, Guests and Rooms, interacts with each other, than it is an unsolved topic.

I had another similar post, where asking for proof for Hilbert’s Hotel.

After rethinking this topic, I want to show you a new example. It tries to show why that the sentence, every guest moves into the next room, hides the fact, that we don’t understand what will happen in this infinite thought experiment (mathematically and logically).

If you don't know Hilbert's Hotel you can read it on Wikipedia:

https://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel

Wikipedia article of Hilberts Hotel captor Analysis:

Hilbert's paradox is a veridical paradox: it leads to a counter-intuitive result that is provably true.

My argument, why I think it is not provable true:

First I want to explain my own example (A), than we go back to Hilbert's Hotel (B): Guest 1 moves out and knocks on Guest 2’s door. Guest 2 goes out. Guest 1 moves in the Room 2 and Guest 2 knocks on Guest 3’s door. Repeat this process every second. If you repeat this forever, there is always one guest n outside knocking on n+1's door. Here we have potential infinity, but never reach infinity. But after an infinite amount of time, every single guest moved. Finally, every guest n has moved in n + 1 Room. No more guest is outside anymore, because all moved. Something happens, which used to be impossible before.

Back to Hilbert's Hotel (B): The mathematical or logical argument for Hilbert's Hotel Paradox is: Every guest can move to n + 1 room. So you can make room for any new guest (Peano axioms).

I would say, there is no logical or mathematical proof, that every single guest will move into the next room in this thought experiment. It's not clear what will happen in this infinity scenario. If you go with my argument, Hilbert’s Hotel is an unsolved topic and not a veridical paradox. Saying every guest moves into the next room in Hilbert's Hotel is like saying every guest moves into the next room in my example (A) above. I am not sure, if every guest moves into the next room, because I don't know how this infinite sets interact with each other. If we don't know how this two infinite sets, Guests and Rooms, interacts with each other, than it is an unsolved topic.