Re: Infinite Meet or no-meets
- From: "Jesse F. Hughes" <jesse@xxxxxxxxxxxxx>
- Date: Mon, 08 May 2006 17:05:46 +0200
"Pubkeybreaker" <Robert_silverman@xxxxxxxxxxxx> writes:
Guy L. wrote:
I am a bit perplexed by the following problem.
Suppose a set of aleph_0 many people are given. Show there is an
infinite subset of that set such that either all the people in the
subset have met one another or all the people in the subset have not
met one another.
How does one go about to prove the above problem? I would ask my
teachers, but none of my teachers at my high school would know...
Let S be your set. Partition it into two disjoint subsets A and B. So
S = A U B.
Let A be the set of people who have not met one another.
I don't see that your set A is well defined. Suppose that our set
consists only of three people (rather than aleph_0). Suppose persons
1 and 2 have met, but no other pair of persons have met.
Then 1 hasn't met 3, so I guess both 1 and 3 are in the set. But 2
hasn't met 3 either, so is 2 in the set or not?
--
Jesse F. Hughes
"There's a thrill that's gone that I'll probably not have in quite the
same way again. After all, FLT was a unique animal, and we had a
great dance." -J.S. Harris on "proving" Fermat's last theorem
.
- Follow-Ups:
- Re: Infinite Meet or no-meets
- From: Pubkeybreaker
- Re: Infinite Meet or no-meets
- From: David Hartley
- Re: Infinite Meet or no-meets
- References:
- Infinite Meet or no-meets
- From: Guy L.
- Re: Infinite Meet or no-meets
- From: Pubkeybreaker
- Infinite Meet or no-meets
- Prev by Date: Re: semilinear transformations
- Next by Date: Re: Fermat's last theorem
- Previous by thread: Re: Infinite Meet or no-meets
- Next by thread: Re: Infinite Meet or no-meets
- Index(es):
Relevant Pages
|
