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Re: Matheology � 047
Posted:
Jun 28, 2012 4:08 PM
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"WM" <mueckenh@rz.fh-augsburg.de> wrote in message
news:aa17866e-0b68-4ab6-8366-4ff68725b1e9@n33g2000vbi.googlegroups.com...
> On 27 Jun., 01:09, "Mike Terry"
> <news.dead.person.sto...@darjeeling.plus.com> wrote:
> > "WM" <mueck...@rz.fh-augsburg.de> wrote in message
>
> > > I prove that in the beginning there are not more than counatbly many
> > > intervals. Then I leave the system.
> >
> > You prove no such thing - there are clearly countably many "removed"
>
> Nothing at all is removed.
Sorry, but in your original example you construct the I_n around the
rational points, and then consider the connected components of the
COMPLEMET. Thus the I_n ARE removed, in forming the complement, although of
course we could express this in many ways without using the word "remove".
However, the meaning is clear, and when you say "nothing is removed" your
just playing a silly word game.
> There are aleph_0 endpoints.
Well, there are aleph_0 intervals I_n, and so obviously that means aleph_0
endpoints...
> aleph_0 is
> countable. The space between the endpoints contains aleph_0 intervls.
The endpoints originally came from a countable sequence of intervals {I_n}.
The obvious meaning of "space between the endpoints" would just be the
original intervals, but you like to state things unclearly, so maybe you
mean something else.
Note that we are talking about your original example with rationals and I_n
here - not your circle example...
> If you do not agree, then you can also construct a Cantir list with
> aleph_0 lines but with more then aleph_0 entries. Do you believe that
> would be possible?
I've no idea what that means. Cantir list??? Maybe you mean Cantor list,
but what's that??? (..in the context of the current thread?)
>
> > intervals I_n, and then you simply *claim* without proof that every
> > "uncovered irrational" is the endpoint of one of the clusters.
>
> In my ring-argument I don't claim mor than given above.
Maybe or maybe not, but in your original "I_n centered on the rationals"
example (to which I was referring) you make such a claim and have never
proved it.
>
> > The problem is that you have NOT presented such a proof, and instead all
> > your purported proofs go round in circles and ultimately just reassert
your
> > original claim without proof!
> >
> >
> I have presentetd a proof that says: If there are uncountably many
> singletons, then they must come into being during the continuous
> process of sliding of endpoints. Matheology must accept that.
> Scientists, in my opinion, will refuse that as wrong.
>
> > I ask you to prove that
> > every uncovered irrational is the endpoint of one of the clusters -
which is
> > no more or less than YOU originally claimed.
>
> There is nothing to prove.
If you don't feel there is anything to prove, fair enough! This is just
confirming what I said above: that you have made wacky claims the you
believe show some problem, and then failed to prove these claims. (...in my
opinion...)
So I'll just ignore your claims as nonsense in that case. (It's easy to
make such wacky claims, and on the internet people do it all the time.)
Others reading your threads are free to reach different conclusions of
course. Perhaps there's a secret army of mathematicians out there who've
been convinced by your arguments! :)
> There are never two irrationals without a
> rational between them. Hence the only alternative is, that there are
> intervals between every pair of irrationals, in particular, there
> cannot be more irrationals than intervals among them. But such tricky
> nonsense as you wrote in your last post will resist any proof.
>
> > In effect your saying "I'm a *special* mathematician who doesn't believe
in
> > completed infinities
>
>
> No, I have proven, given continuous sliding is not a discontinuous
> process with respect to the intervals between endpoints, that the
> assumption of completed infinity is false.
Rubbish. I've recently responded to one of your "sliding ring" posts, and
the essence of my response is that you've constructed some complicated (but
basically quite OK) scenario and then concluded there is some mysterious
contradiction at work, whereas in fact you've YET AGAIN just made some
unproven assertions based on your faulty intuition about the situation.
I predict that as with your original I_n claims you will not even make a
serious attempt to turn your claims into a proof. (Probably you will say
your claims are "self-evident", although only you will consider them such...
Anyway, you can respond in my other post if you want to continue.)
>
>
> - that means I can make mathematical claims without
> > needing to prove them." Well that's not how maths works - you still have
to
> > prove your claims, and of course (you being you) I'd expect you to
construct
> > your proof without using completed infinities!
>
> No. The proof that sqrt(2) is irrational stars with the assumption of
> rationality and then contradicts it. So do I with finished infinity.
Only in your own mind, but maybe that's enough for you?
Perhaps you should consider submitting your proof to a respectable
peer-reviewed journal? After all, it seems your proof (if valid) would be
of huge interest to mathematicians world wide!
Mike.
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