Date: Jul 11, 2013 10:53 AM
Author: David C. Ullrich
Subject: Re: Problem understanding proof of Jordan Curve Theorem

On Thu, 11 Jul 2013 00:53:42 -0700 (PDT), wrote:

>On Wednesday, July 10, 2013 5:02:59 PM UTC+1, wrote:

>> It's clear.
>> The proof I'm about to give is "perfectly clear" in my book. It
>> may strike you as something that he should have written
>> out in detail because it's not obvious. I disagree - it
>> was immediately obvious to me, and the paper was
>> written with a certain audience in mind...

>But I never said anything remotely critical of the author or the paper. I made the factually correct statement that the lemma was not clear _to me_.
> What you've done is to arbitrarily come up with a statement that you disagree with, and then to explain your disagreement.


Why do you spend so much time on this sort of thing, debating
nuances of who said what about who said what about who
said what?

I said you _may_ disagree that the argument I was going to give
was not clear. Where by "clear" I meant that it really was
sufficient for the author to simply state that the existence
of a maximmizing disk was clear, without giving any

One reason I thought you might feel that way was
various things from the past, where you've said something
was not clear and insiisted that the author should have
provided more explanation.

Another reason is that the assertion _was_ perfectly
clear! The author says the existence of a maximizing
disk is clear. You say it's not clear to you. The proof
I gave didn't involve any sublety or cleverness - it
was the sort of thing where when I ask myself
how I'd prove that I saw the proof immediately.

So if you say the assertion is not clear to you
then either (i) the proof I gave was not clear to
you, the possibility I mentioned, or (ii) you didn't
see that proof until I pointed it out.

The reason (i) seemed likely to me is that I
didn't see how (ii) was possible! You start with
what you're trying to prove, think about it
for a second, and you have the proof.

>I could follow in your footsteps by saying that I disagree with the statement that English is the most commonly spoken language in Singapore.

You _really_ think that's a fair analogy?

>On the maths side, the help given by yourself and Rupert is greatly appreciated and I now fully understand why the remark in lemma 3 that I referred to is correct.

Which remark? There's no "remark" that there exists a
maximizing disk. There _is_ a remark to the effect that
the existence of a maximizing disk is _clear_.

The reason I ask is actually to help you out, whether
you believe it or not. You're trying to learn some math.
That's good. If the existence of a maximizing disk is
not "clear" then you really need to get better at
finding proofs of trivialities.

Which is why skipping most of the exercises in
Rudin was not a good idea. It's not too late...

>Thank You,
>Paul Epstein