Re: Cantor and the binary tree

mueckenh@xxxxxxxxxxxxxxxxx writes:

> David Kastrup wrote:
>
>> > Look here: The natural number n e N is nothing else than an
>> > abbreviation of its initial segment {1,2,3,...,n} c N.
>> > N consists exclusively of elements n. Similarly N consists exclusively
>> > of subsets = initial segments (all of which include 1). There is no
>> > element of N which is not an element of such a subset. And there is not
>> > a pair of different elements n and n' of N, which satisfy the following
>> > condition:
>> > n belongs to an initial segment S which does not contain n'
>> > and
>> > n' belongs to an initial segment S' which does not contain n
>> > in short:
>> > n e S and n' !e S and n' e S' and n !e S'.
>> > As this requirement is impossible to satisfy, the segment of n includes
>> > all elements less than n. This holds for any n e N. Therefore N is a
>> > segment.
>>
>> Nope. Your "Therefore", again, is a piece of [censored] and a non
>> sequitur. There is nothing whatsoever to the left of this "Therefore"
>> that would justify the conclusion.
>
> The conclusion is justified by the bijection of n on its initial
> segment.
> There is no largest n, so there is no largest segment. But any n is
> finite, so any segment is finite. Outside of segments there are no
> natural numbers.
> *Therefore* the set of all n, called N, is a segment.

Again, misuse of "therefore". Outside of segments, there are no
natural numbers, but that does not mean that N is a segment. It
merely means that N is the union of all segments. You have not proven
that the union of an _infinite_ number of segments is again a segment,
and indeed you couldn't.

And indeed, it is the mark of a "segment" in your use of the word that
it contains its largest n. To quote yourself: "there is no largest n,
so there is no largest segment". So N can't be a segment, by your
very own words.

> PS: You will not prevent this obvoious fact by cursing and
> shouting.

I don't need to curse and shout. You contradict yourself already.
You are just too stupid to realize it.

> So stop foaming and leave things as they are.

Good advice, you ought to heed it.

> But you will keep on swearing like a trooper, I know. The only
> question is, why can't you and Hughes behave like civilized persons?

Calling "hogwash" "hogwash" is not uncivilized. Anyway, civilization
is marked by increasing the knowledge of your culture and building
upon it. You are too stupid to even fathom the current state, and are
actively trying to destroy it by teaching complete nonsense to your
disciples.

This is the mark of an illiterate caveman by choice and malice,
someone who is so jealous of living and dead persons' intellects that
all he can think of is to spread incoherent nonsense about them and
hope that nobody notices.

You are the last person fit to talk about civility.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
.