Re: Is continuum completely filled up?


"Zim Olson" <zimolson@xxxxxxxxxxxxxxxxxx> wrote in message
news:11914973.1168554892750.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxxxxx
I am biginer in English and mathrmatics.
If real line is filled with points and each point is
distinguished,then each point has difference from
every other points.
Therfore real line has void.

Thanks for advance.


Hello:

I am not sure the point One exists between the points zero and two. Unless
you are trying to represent something in particular with the number line.

Sorry.....I just look at the Number Line as a Math Construct only, used to
model only ...existential items such as in Time and Space etc.

Zim Olson
http://www.zimmathematics.com

My idea is not so conclete at present . What I want is to remove inproper
concepts and partiality from mathematics ,and make it more consistent .
What I meant is not that a line is constructed from unit intervals ,but
that line is subdivided endlessly ,and each subdivision remain as intervals
..
It seems to me that there are partial treatment in mathematics .
Open set looks strange for me .
When the boundery is removed , unspecified points in its neibourhood are
remained .
I think that there must be boundery from external points in unspecified
points .
Why can only original boundery be specified .
In my idea ,points are regarded as mark on the object .
We can only subdivide a line ,but a line is not constructed with points .
The operation of subdivision dont ends . this is the reason why points
around the limit point
cannot be specified .
I admit only marking as an operation on interval .
We can make some assumption on reals to make nit ordered field .
But ordered field is the relation between numbers ,and the relation of it
with a geometric line is another question .
When we deal with open set ,actual treatment doesn't differ from traditional
one .
How much add points on a line , its remained space is, as it was , that is
infinite .
This circumstances is the same as that how far we may go ,the remained
distance is unchanged .
I don't admit difference between these two infinity , and remained time for
rotating ball without any resistance
I don't think that my idea is so much different from traditional one in
actual operation .
Main difference is this .
How much points of division increase ,its amount is measure zero , even
accounting reals .
Each interval may be considerd as infinitesimal ,if one please .
A line may be subdivided beyond reals .
But I rather prefer to regard it 0 , at the limit in the range of reals
,under the assumption that values of each degit of decimal numbers lose its
meaning , according to its unit approach the infinite .
And each numbers are undistinguishable in its smallest limits of
neighborhood .
Nevertheless , we can manipulate countable number of reals from among them
as before ,
and its measure is calculated as the amount of intervals .
..That is, We can do ordinary operation with counterble number of elements .
The rest except these , it seems like to me that only their existance are
assumed so far ,too .
Proof that square root of 2 is not rational is done using fraction of finte
numbers .
In the case considering the limit , the boundery between rationals and
irrationals is not clear
These are brief sketch of my idea . I t may have many flaws , but this is
also my cognition about infinity .
Thanks for your question , I have seen your HP before , this is unexpected
pleasure .

Regards
Ozaki Tosiaki








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