Re: Infinite Meet or no-meets
- From: "Pubkeybreaker" <Robert_silverman@xxxxxxxxxxxx>
- Date: 8 May 2006 06:40:06 -0700
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.
If A is empty then..........(conclude something about B)
If A is non-empty but finite then..... (conclude something about B)
If A is infinite then the problem is authomatically satisfied......
.
- Follow-Ups:
- Re: Infinite Meet or no-meets
- From: Jesse F. Hughes
- Re: Infinite Meet or no-meets
- References:
- Infinite Meet or no-meets
- From: Guy L.
- Infinite Meet or no-meets
- Prev by Date: Re: what is a cardinality of the sets?
- Next by Date: Re: question about Rudin's 3.2(a)
- Previous by thread: Infinite Meet or no-meets
- Next by thread: Re: Infinite Meet or no-meets
- Index(es):
Relevant Pages
|
