Re: Is continuum completely filled up?


"Saurav" <saurav1b@xxxxxxxxx> wrote in message
news:1168618358.480689.156430@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

The collection of intervals is something else than what we in topology
consider to be the space. You probably know that if we deal with
topological aspects, the collection of interval becomes something we
call the "basis" of the topology.
Well, if you are not satisfied to view a line as the collection of
points, I must allow you to have your own opinion. But in that case,
you have got to construct a new kind of topology.
A line is, in as much as we comprehend presently, regarded as a
linearly ordered set of points; and the collection of intervals
generate a unique topology on it, called the "order topology". To
construct in your own way, I think, you shall have to review the whole
conception of order topology and their related theorems.
I recommend a paper, by van Douwen, entitled "The Horrors of topology :
a nonnormal orderable space". This will make you understand how
critical it is to deal with even our present conception of order
topology; if you pioneer a new conception, remember, you'd have to
construct a parallel, vivid, more appealing theory of this.
You may think that a line is endlessly subdividable substance for me.
I think that the apprecation of my idea to reals and a line is not so
different from traditional treatment in essencial part
I didn't know about order topology.

I want to ristrict our argument in the range of ordinary language .
But ordinary language does in no way impede you from using transfinite
induction, and if you take "ordinary language" for a literal language,
I am afraid you'd fall through to put even a smidgen of your intuition
into considerably unambiguous form.
I try to use formal language as long as possible.

See, what you mean by cutting is indeed a finite recursive process. You
cut nth time, then (n+1)th time. There is hardly any limit ordinal
there. But in cutting a continuous object, of whose the cardinality
surpasses d, there is a need to cut "omega'th" time; how could you
manage to do that?

What I intended to say, is wheather a line is build from points or not.
Why point of measure 0 gather up to produce measure or lengh? Zeno's problem
have been solved, that is hypertask?
About other my argument also , I want to know why some theory of
mathematics
is different from our intuition .

What actually our intuition tells us is not that much clear.
To examine how much our intuition is expressible in mathematics, is one of
my purpouse too.
I want that mathematics can expresse things naturally as far as possible
..
I talk about what I took doubt about mathematics , because I want to
know
why the matter is that .
Right, you should think how they are as they are, this is actual
philosophy. Thank you.
I want to think a line not as collection of points , but that of
intervals .
I don't know wheather this idea goes well or not .
Read what I've written above. Your ideas ->might<- go well, but in
order to do that, you've got to toil.
Thant you for informing various article to me.

NOT "provably", it has a different meaning, may be you meant
"probably".
that there don't exist uncountable
number of objects (or we cannot deal with them ).
There is much research on this. I myself am not sure what indeed has
created the problem. But as far I can tell you, "a is countable" may
have two meaning:
1) { x | x in a } is countable;
2) { x | M |= ( x in a) } is countable, where M is a particular model.
May be you already know this.
So that I thougt that
countable model only is sufficient to descrive a theory .
This is very controversial. You may read the thread

http://groups.google.co.in/group/sci.math/browse_frm/thread/122db6710267970b
/c23b753fb8a4ecb3?lnk=gst&q=Saurav&rnum=2#c23b753fb8a4ecb3
Though this doesn't directly deal with the problem, I hope there is
something that relates to this problem.

I don't know what sort of thigs you imagined from what I said .
But for this question, my answer is that because I think , then I exist
..
Who told you this answer? It is not you that has said this first, as I
know; but the implication is not clear. Who said, again, that you
think; and who said, that if one thinks then one exists?
I don't know how Decartes said his words correctry in English and what
opinion do you have about this statement. What I meant is that regardless of
any
arguments about myself, I realise what I am.
Provabley we all are finite and mortal , so that , I know that I can not
complehend the Universe .
You _know_ that? How?
What is the Universe? I had thought that we have some common recognition
about
this concept.
But I am in the Universe as well as you ,and communicating with you .
Probably you have read Russell's Paradox. You can not say " I have the
property p". For example, if you say " I am lying", are you lying
indeed? In view of this, you can heardly say, no matter how much urge
may you feel to utter it, "I am in the universe".
If you deny it , no communication is realised .
Don't take your decision so readily!

Regards
Ozaki Toshiaki





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