Re: Infinite Meet or no-meets

David Hartley <me9@xxxxxxxxxxx> writes:

In message <87r73436b9.fsf@xxxxxxxxxxxxx>, Jesse F. Hughes
<jesse@xxxxxxxxxxxxx> writes
"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?


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......

I think the intention is that A should be a *maximal* set of people
who haven't met each other. (Everyone will be in such a set.) Everyone
in B has met someone in A, so if A is finite, someone in A has met
...

Sorry, I still don't get it. If A is just some maximal set of folks
that haven't met each other, then the complement of A is *not* some
set of folks who have met every other guy in the set.

Is it?

--
"It's my belief that when religion and pseudoscience achieve an
official status within a culture [...], then genocide, war,
oppression, injustice, and economic stagnation are sure to follow."
-- David Petry, on why |X| < |P(X)| is bad, bad, bad.
.

Relevant Pages

  • Re: Infinite Meet or no-meets
    ... Jesse F. Hughes wrote: ... infinite subset of that set such that either all the people in the ... teachers, but none of my teachers at my high school would know... ...
    (sci.math)
  • Re: Infinite Meet or no-meets
    ... infinite subset of that set such that either all the people in the ... teachers, but none of my teachers at my high school would know... ... I don't see that your partition helps us do that. ... part of who I am is an endless amount of energy as long as there is ...
    (sci.math)
  • Re: Infinite Meet or no-meets
    ... infinite subset of that set such that either all the people in the ... teachers, but none of my teachers at my high school would know... ... "There's a thrill that's gone that I'll probably not have in quite the ... After all, FLT was a unique animal, and we had a ...
    (sci.math)
  • Re: Infinite Meet or no-meets
    ... Jesse F. Hughes writes ... infinite subset of that set such that either all the people in the ... teachers, but none of my teachers at my high school would know... ...
    (sci.math)
Quantcast