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Replies: 15   Last Post: Apr 25, 1995 5:26 PM

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 Ronald A Ward Posts: 298 Registered: 12/4/04
Posted: Apr 18, 1995 7:57 PM

Jill,
take-off on George Gamow's "An Infinity of Guests"?

INTRO: "Let us imagine a hotel with a FINITE number of rooms,
and assume that all the rooms are occupied. A new guest arrives and asks
for a room. 'Sorry,' says the proprietor, 'but all the rooms are
occupied. So unless you want to share with someone, I can't accomodate
you.'"
FIRST PROBLEM: "Now let us imagine a hotel with an INFINITE
number of rooms, and all the rooms are occupied. To this hotel, too,
comes a new guest and asks for a room. 'But of course!' exclaims the
proprietor. What one simple instruction could the proprietor give once on
the hotel intercom, so that each guest already in the hotel would know what
to do, and so that a room would be opened for the new guest, but in such
a way that no one would have to share a room and everyone could be
accomodated?"

SECOND PROBLEM: "Let us imagine now a hotel with an INFINITE
number of rooms, all occupied, and an INFINITE number of new guests
proprietor. What one simple instruction could the proprietor give once
on the hotel intercom, so that each guest already in the hotel would know
what to do, and so that infinitely many rooms would be opened for the new
guests, but in such a way that no one would have to share a room and
everyone could be accomodated? To which hotel room would guest number 50
in line go? How about the 1000th new guest?"

I believe this problem may have originated with the German mathematician
David Hilbert. It is do-able and of interest to gifted youngsters of the
age you will be working with.

If you're looking for something more ACTIVE, I can also recommend a
number of playground math games, but they won't deal with infinity.

Ron Ward/Western Washington U/Bellingham, WA 98225
ronaward@henson.cc.wwu.edu

On Mon, 17 Apr 1995, Jill A. Dumesnil wrote:

> I'm an Assistant Professor of Mathematics who has been asked to
> prepare 45 minutes to an hour of "meaningful enrichment activity" for
> gifted and talent fifth graders for this friday. The short notice
> and my inexperience with elementary-aged children has me a bit
> anxious. All of my experience has been teaching college mathematics.
>
> I'm thinking of doing something basic on the concept of infinity and
> the different "sizes" of infinity. It's been my (extremely limited)
> experience that it's "easy" to convince children that there are
> infinitely many real numbers between 0 and 1 by considering the
> unitary fractions (with numerator 1). They quickly see that there
> are infinitely many of these and "many more" numbers than these
> between 0 and 1. Does anyone have any ideas for activities or
> materials that I could use? I appreciate your help.
>
> ---
> Jill A. Dumesnil
>
> Stephen F. Austin State Univ.
>
> Dept. of Mathematics and Statistics
>
> Nacogdoches, TX 75962-3040
> dumesnil@math.sfasu.edu
>
>
>
>

Date Subject Author
4/17/95 Jill A. Dumesnil
4/17/95 Ken Blystone
4/17/95 Andre TOOM
4/17/95 David Wang
4/18/95 Lou Talman
4/17/95 Hannah Slovin
4/18/95 Linda Coutts