I disagree with Thrawn here. I think the problem is that he does not fully understand the puzzle. Moreover, there actually do exist more formal ways to make the Hilbert Hotel problem more precise. But the problem with what he/ she says is that NOBODY IS SAYING THAT PEOPLE ARE BEING MOVED TO HIGHER ROOMS BEYOND THE EXISTING ONES. In effect, he is arguing against a strawman.
Thrawn has basically made an ipse dixit assertion that something does not make sense. But not making sense can be a limitation on the perceiver, and not necessarily on the message. Although I agree that equivocation can be a problem (e.g., when religious people try to smuggle in the word "faith" for people's confidence or trust in everyday life to argue that faith is useful), it is NOT relevant or applicable here. In the case of the original, much easier Hilbert Hotel problem, one has every room filled and one person comes along. The classic solution to this simpler puzzle is to have each person move to the room with number 1 higher, thus opening up room 1. Nobody is left out in the cold, and there is no "higher number than infinity" type problem that Thrawn seems to worry about.
I reiterate that I will share my solution with anybody who writes me at DrMWEcker@aol.com (that's DrMWEcker at aol dot com). I also will try to remember to come back here to post my solution here AFTER it is published in my column in MathAMATYC Educator.
(Dr. Mike Ecker is a PhD mathematician, a retired math professor, and the problem section editor of the mathematics journal MAE.)
I disagree with Thrawn here. I think the problem is that he does not fully understand the puzzle. Moreover, there actually do exist more formal ways to make the Hilbert Hotel problem more precise. But the problem with what he/ she says is that NOBODY IS SAYING THAT PEOPLE ARE BEING MOVED TO HIGHER ROOMS BEYOND THE EXISTING ONES. In effect, he is arguing against a strawman.
Thrawn has basically made an ipse dixit assertion that something does not make sense. But not making sense can be a limitation on the perceiver, and not necessarily on the message. Although I agree that equivocation can be a problem (e.g., when religious people try to smuggle in the word "faith" for people's confidence or trust in everyday life to argue that faith is useful), it is NOT relevant or applicable here. In the case of the original, much easier Hilbert Hotel problem, one has every room filled and one person comes along. The classic solution to this simpler puzzle is to have each person move to the room with number 1 higher, thus opening up room 1. Nobody is left out in the cold, and there is no "higher number than infinity" type problem that Thrawn seems to worry about.
I reiterate that I will share my solution with anybody who writes me at DrMWEcker@aol.com (that's DrMWEcker at aol dot com). I also will try to remember to come back here to post my solution here AFTER it is published in my column in MathAMATYC Educator.
(Dr. Mike Ecker is a PhD mathematician, a retired math professor, and the problem section editor of the mathematics journal MAE.)