Re: Kuratowski Ordered Pair

On Dec 19, 2:54 pm, Hero <Hero.van.Jind...@xxxxxx> wrote:

As a term is here an expression of set theory, a proper one, and let p
denote a set,
than this term
......p.... is build with the symbol p.

So you mean 'p' is an individual constant or 0-place function symbol
or 'p' is any term of the language?

But let it be explained in another way :......u..... are the elements
of a set
{.....u .....} , which is a superset of u, or a superset of a superset
of u, and so forth a finite number of times.

You said ....u.... was a term. Now you it's "elements" of a set.

and { -----u-----} is a different superset, or superset of a superset
of u

So f.e. {....u ....} can be { u } , or { u, { u } } or { { } , { u ,
{ } } , { v } } in which v is another set. And {---u---} is a
different one of these.

Hmm, I guess you mean ....u.... is some nonempty set, such that, if we
"finitely drill down" far enough, we get u "nested" somewhere within.
I think that can be formalized in set theory (using transitive closure
or something like that). So, okay, let's see...

And why this ?
I get from it this generalisation of all definitions of ordered
pairs, i have seen so far:
<p, q > := { { ....p....} , { --- q---} }

Hmm, I guess you mean that the various different definitions, such as
Kuratowski, Weiner, etc, are of the above form?

It becomes a set, when You
insert two different proper terms.

WHAT is a set? You've given a general schema for a class of terms.
Yes, for EACH instance of the schema we get a term (which, upon
interpretation and assignment of values to variables) denotes a set.
Is that what you mean?

{ p } is a superset of p

There's no such generalization in Z set theory. Quite the contrary.

It is NEVER the case that

p is nonempty and { p } is a superset of p .

and { p, q } is a superset of q,

Similar as above.

so i have
one example of the generalisation < p, q >, in this case { { p }, { p,
q } } the following argument is about.

Okay, we're back to Kuratowski. So, now, what is your argument when
you say "the following argument" with regard to the Kuratowski?

Meanwhile, it would help GREATLY if you would tell me what are some of
the books on the subjects of mathematical logic, set theory, strings,
and sequences you are informed by, so I can try to get hold of those
books so that I can better follow along what you're saying.

As this is a discussion not about me, but about Kuratowski's
definition, so my level doesn't matter much in here. Books are still
of some importance, but not everybody has a library or the money to
buy around. So in a life discussion it might be better to refer to
math in the web, available at a click, or just cite from the books, as
i have done with Hamilton's Theory of Pure Time.
But in case You want to have some background about me personally,
google for my postings in sci.math and de.sci.mathematik or take a
look at my website ( mainly about complex numbers):http://1iz.de
You are welcome.

That answer really pisses me off, and I'll tell you why:

(1) I am offering to consider your arguments, which is work for me,
because you are using EXTREMELY idiosyncratic notation, which you
cannot fairly expect me to understand without some work. I said that
it help ME if I knew where you notation is coming from. I didn't even
say that it is a fault that you're using such notation, but rather I
asked you to HELP me to UNDERSTAND you by letting me study whatever
this notation is of yours or the source of wherever you're getting
your mathematical basis.

(2) I didn't even say you have to go out and get books. I just asked a
simple, direct question as to what books *I* can get to catch up to
your notation and your mathematical context. I offered to go out of MY
way to look at whatever books would help me better understand you. But
you REVERSED that to make it look like I asked YOU to look at MY
books.

(3) If your notation and basic mathematical context is not in any
books, then all you had to do is just say that. Then I would point out
that you can't expect me to absorb your extremely idiosyncratic
notation and any of your ersatz notions without difficulty, since
you're not giving me any other mathematical context by which I can
understand your post.

(4) And even though I did NOT say you need to read a book on set
theory, it has NOW become apparent that you, since you have completely
mistaken notions such that {p} superset of p.

(5) My question was for the purpose of finding out how I can better
understand what it is you're trying to say. But instead of accepting
that, you just dug in your heels in a way that now makes COMMUNICATION
even more difficult.

(6) Reading different postings by you or articles on various subjects
is a LOT OF WORK for me just to understand your idiosyncratic
notation. All I asked for was where I could find such notation
EXPLAINED as notation or in action in some SYSTEMATIC treatment. On
the other hand, YOU are the one who wants to challenge some
mathematics that is already abundantly explained in all kinds of
books, so, if you were REASONABLE, then you would AT LEAST learn
enough of what it is you're CRITIQUING so that you know how it works.

So, *I* don't need to take MY time and energy to follow your fractured
notation and arguments. If YOU want me to understand YOU, then you
need to do what other people who are sincere do - lay out your
notation and your notions in a systematic manner that RESPECTS the
reader by giving him or her a lucid account, not just a bunch of
fractured notation, just as such fair and reasonable accounts are
given in ordinary mathematical communication.

It's your call. Respect me by giving me a lucid and systematic account
of your idiosyncratic notation (and not just drop even more
unexplained notation into the conversation) or be content for the
conversation to end in a mire of confusions.

MoeBlee

P.S. And I went to your web site. No help at all in figuring out what
it is you're trying to say in this thread.


.

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