Link: http://jcdverha.home.xs4all.nl/scijokes/1_6.html
And a further correction as quoted by Nils B.:
"You've perhaps heard from 17,000 mathematicians since this section was quoted in the 2005 Jan "Notices of the AMS", but while splitting hairs, this definition of compact is incorrect: it defines -totally bounded-, not compact. For instance, the -open- interval (0,1) is totally bounded (can be guarded by a finite number of policemen, no matter how nearsighted a policeman is) but not compact."
Alright, now we have to close this city :>
further correction: Level א_①
Clearly, these policemen need to start scheduling appointments with an optometrist.
That shouldn’t be a problem as there are only finitely many of them. However, for unbounded cities, it would make sense to introduce a large building where infinitely many optometrists can work? I propose to call it Mike’s Medical Centre.
I dunno. I still think the height of logic was when I and a mathematician recreated a problem he'd seen in a journal, not from the answer, but from remembering the FORM of the answer. That was enough information to recreate what the question and answer must have been. It was about October 2000--I also remember the Car Talk Puzzler we discussed.
What do you think about the following definition (of the compact city)?
When all the citizens guard their neighbours, almost everyone can sleep happily.
(of course, the neighbourhoods are open)
Level infinity?
But what kind of infinity?...
All these police officers now work for MLB as umpires.
A city for which, were it guarded effectively by an infinite number of nearsighted policemen, you could fire all but a finite number of them in such a way that they can still guard it effectively without any change in their individual duties?
Not sure I get this - is the last definition a 'uniform' nearsightedness of policemen? (otherwise I don't get it)