## A Conversation for Infinity, and the Infinite Hotel Paradox

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### Flea Market: A414523 - Infinity, and the Infinite Hotel Paradox

Zak T Duck Started conversation Oct 4, 2000

http://www.h2g2.com/A414523

Has the whole of h2g2 gone paradox mad or something recently? I found this little gem relating to the Hilbert's Infinite Hotel Paradox. The only problem is that Calroth's userspace (the guy who wrote the article) doesn't appear to have been visited by its owner for nearly two months, so whether my points I made in the entry's fora will go noticed I do not know. If not then I suppose any good SubEd will taker the points on board.

I also noticed a few other promising entries on Calroth's userspace so I'm off to have a look at those too.

Croz (Scout)

### A414523- Infinity, and the Infinite Hotel Paradox

Gnomon - time to move on Posted Oct 5, 2000

This entry is interesting but it is very much incomplete. The Hotel Paradox was devised as a method of illustrating Georg Cantor's mathematical theory of countable and uncountable sets. This is a mind blowing but not very difficult branch of mathematics. The Hotel Paradox needs to be presented as part of this, not just on its own. Are there any mathematicians out there with time to spare to tell us about Cantor? Or will I have to do it myself?

### A414523- Infinity, and the Infinite Hotel Paradox

J'au-Ã¦mne Posted Oct 5, 2000

Actually there are variously entries on 'Cantor's diagonal argument' http://www.h2g2.com/A383915 and 'What I don't like about Cantor's diagonal argument' http://www.h2g2.com/A386787

Maths being a joyful subject... read http://www.h2g2.com/A384284 the project on numbers and logic

### A414523- Infinity, and the Infinite Hotel Paradox

Martin Harper Posted Oct 5, 2000

ooh - that's good. Seems like it would be a nice addition to the guide - if anyone writes an entry on Cantor and suchlike they can link to it (and vica versa), but until then it seems fine as is until that moment...

### A414523- Infinity, and the Infinite Hotel Paradox

J'au-Ã¦mne Posted Oct 5, 2000

Its a good entry as far as it goes, but either the original author or someone else needs to finish it...

### A414523- Infinity, and the Infinite Hotel Paradox

Dogster Posted Oct 5, 2000

The "What I don't like about Cantor..." argument is wrong though (which is worth bearing in mind). If anyone's interested I could write a Cantor entry, but the "Cantor's diagonal argument" entry seems pretty complete. The only thing that would be worth adding would be a slightly more mathematical footnote perhaps?

### A414523- Infinity, and the Infinite Hotel Paradox

Gnomon - time to move on Posted Oct 6, 2000

Cantor's diagonal argument shows that there is an infinity which is uncountable. The Hotel Paradox explores the other infinity, the countable one. I was looking for some of the mathematics that goes with the countable infinity, rather than launching straight into the diagonal argument.

### A414523 - Infinity, and the Infinite Hotel Paradox

Martin Harper Posted Oct 6, 2000

I don't understand - why can't we have an entry that explores countable infinity in this sort of informal style? It's informative, it's factual, it's complete. Yes, there is info relevant to it that's not in the guide yet - but that's true of all subjects - we had an entry on knives before there was one on forks, remember?

### A414523 - Infinity, and the Infinite Hotel Paradox

Gnomon - time to move on Posted Oct 6, 2000

You're right!

I'd settle for a few sentences at the end tidying it up and relating to Cantor's theory of countable infinity.

### A414523- Infinity, and the Infinite Hotel Paradox

Calroth Posted Nov 17, 2000

I'm here!

Sorry about being away... you know how university exams are

I'm quite prepared to assume control of my articles again (and I haven't even looked at my other entries to see what's been Recommended yet). It's a great honour and buzz to have been picked out of obscurity for this.

There have been a lot of good points made, and I'm still wondering where to draw the line between technicalities and laymanship. I'm vaguely familiar with Cantor's paradox too, so we'll see where that fits in.

So hold on, I suppose!

### A414523- Infinity, and the Infinite Hotel Paradox

Monsignore Pizzafunghi Bosselese Posted Dec 10, 2000

I've just called Jaz (http://www.h2g2.com/U161306), he's preparing an entry on the Cantor Set at http://www.h2g2.com/A479739

keep on the good work!

### A414523- Infinity, and the Infinite Hotel Paradox

Joe aka Arnia, Muse, Keeper, MathEd, Guru and Zen Cook (business is booming) Posted Dec 16, 2000

Set theory is getting a going over then.

Anyone want to help with algebraic structures, great mathematicians I or Introductory Algebra also?

We are looking for mathematicians!

### A414523- Infinity, and the Infinite Hotel Paradox

Martin Harper Posted Dec 16, 2000

But you'll settle for anyone?

myre - "PR is like a sewer - what you get out of it depends on what you put into it"

### A414523- Infinity, and the Infinite Hotel Paradox

Joe aka Arnia, Muse, Keeper, MathEd, Guru and Zen Cook (business is booming) Posted Dec 16, 2000

### A414523- Infinity, and the Infinite Hotel Paradox

Martin Harper Posted Apr 6, 2001

Calroth! Calroth! Wake Up!

Oh dear. I think this entry is going to have to go to the workshop - it's an uncomplete work - as shown by the "stay tuned" at the bottom - and there's more that can and should be said about infinite hotels.

I hope he comes back after the mailshot...

### A414523- Infinity, and the Infinite Hotel Paradox

Zak T Duck Posted Apr 7, 2001

I'm inclined to agree. It's a real shame Calroth isn't around to complete this, it would have proved an intersting topic for inclusion. Oh well, off the the workshop it is then. Perhaps someone else will show a bit more enthusiasm with it.

### Thread Moved

h2g2 auto-messages Posted Oct 15, 2001

Editorial Note: This conversation has been moved from 'The Writing Workshop' to 'The Flea Market'.

...as the author of this entry seems to have 'left the building'.

### Thread Moved

Spike Anderson is sorry he can't catch up on a whole month's backlog Posted Feb 28, 2002

### Thread Moved

Spike Anderson is sorry he can't catch up on a whole month's backlog Posted Mar 1, 2002

Here it is, but it's just a placeholder for now: A702730.

-Spike A.

Key: Complain about this post

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### Flea Market: A414523 - Infinity, and the Infinite Hotel Paradox

- 1: Zak T Duck (Oct 4, 2000)
- 2: Gnomon - time to move on (Oct 5, 2000)
- 3: J'au-Ã¦mne (Oct 5, 2000)
- 4: Martin Harper (Oct 5, 2000)
- 5: J'au-Ã¦mne (Oct 5, 2000)
- 6: Dogster (Oct 5, 2000)
- 7: Gnomon - time to move on (Oct 6, 2000)
- 8: Martin Harper (Oct 6, 2000)
- 9: Gnomon - time to move on (Oct 6, 2000)
- 10: Calroth (Nov 17, 2000)
- 11: Monsignore Pizzafunghi Bosselese (Dec 10, 2000)
- 12: Joe aka Arnia, Muse, Keeper, MathEd, Guru and Zen Cook (business is booming) (Dec 16, 2000)
- 13: Martin Harper (Dec 16, 2000)
- 14: Joe aka Arnia, Muse, Keeper, MathEd, Guru and Zen Cook (business is booming) (Dec 16, 2000)
- 15: Martin Harper (Apr 6, 2001)
- 16: Zak T Duck (Apr 7, 2001)
- 17: h2g2 auto-messages (Oct 15, 2001)
- 18: Spike Anderson is sorry he can't catch up on a whole month's backlog (Feb 28, 2002)
- 19: Martin Harper (Feb 28, 2002)
- 20: Spike Anderson is sorry he can't catch up on a whole month's backlog (Mar 1, 2002)

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