Re: Is continuum completely filled up?


toshiaki wrote:
"Hero" <Hero.van.Jindelt@xxxxxx> wrote in message
news:1168684524.129904.50640@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
toshiaki schrieb:

.
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....

You are at the point, where You should read, what other people said
about it here, but elsewhere too.
You have a line, points - and you have numbers. There is the story of
Achilles and the tortoise, and the story of the arrow, who can not fly
for logical reasons - thought about by Zeno. This brings about movement
and time. Numbers can reveal some structure of the flow of time as
well, and time is not a geometric object or a line - as it seems to
some people.
http://history.hanover.edu/texts/presoc/zeno.htm
Time, movement, independent and dependent variable values - with this
people like Leibniz, Newton were developing the calculus. Here You have
to consider the infinite small value. Is it zero? ( I think yes. It has
a value different from zero when it is in relation to another infinite
small value :
dx = 0, dy= 0 , but dy / dx = 3, when y = 3*x).

Give this a mathematical foundation, You have people like Cauchy, Karl
Marx.
And to the topological properties of a line You can look for
Kuratowski.

Nowadays a lot of mathematicians seems to freeze up movement, taking
the trace of a movement for the movement itself.
You are writing in the moment like giving single sounds, try to make
some music out of it.
Have pleasure and success with it.
Hero

My thougt about infinity began with experience in my childhood and the
mystery of Zeno.
The chain which the race of tortoise and Achillese produce increasingly
small, but when magnified, it is still the same chain as it were.
They are at start line still now.
von Neuman comented about Zeno, that why he didn't think movement as
function of time?
But, he only persued movement of Achilles and tortoise ,and not made them
move.
Then, Zeno is right?
No, unending chain is not evidense of impossibility of motion.
He only showed that the real existence is beyond our logic.
I don't know whether Achilles can catch up with tortoise having run through
Zeno's chain.
But when time would end, this problem would certainly have been solved.
dx = 0, dy= 0 , but dy / dx = 3, when y = 3*x).
I didn't know that dx and dy can be set zero. I only knew that d_{a}f
is a linear functional : h |---> h.f'(a). Where did you see such
things: dx = 0, dy = 0, yet dy/dx is is a real number?
As for this, traditional formula of differencial is sufficient, with no need
of unspecifiable number.
dy/dx = lim(h- > 0){3*(x+h)-3*x}/{(x+h)-x}
Caudhy is one of mathematician that I most respect . He avoided to assume
things we cannot see.
He dealt with only visually representable objects, and discribed its
behavier in observable range.
(x ->oo) =>(1/x ->0), ( x ->oo) =>(1/x ->0)^(1/x^2 ->0)^{(1/x)/(1/x^2) =
x=>oo }
The ratio of objects don't change depending on scale.
His work is full of concise and essensial theorem.
He difined reals as the equevalence class of Cauchy sequences. His
diffinition doesn't necessarily imply the existance of uncountable number of
reals ,though it correspond to power set of rationals.
Karl Marx said that scholars interplit histry, but I will create histry. And
Ludwig Witgenstein said that the work of philosophy is to correct
misunderstanding.
Isn't it the same string I harped on again and again?
When I read this phrase for the first time, I thougt that therefor
philosophy is not interesting. But, what I am doing is to exercise this.
I am studying elementary mathematics now, to examine whether I can
reformulate it with my idea.
Trough discussion here, my idea has became clear gradually, from mysty dout.
Thank you for timely suggestion.

Regards
Ozaki Tosiaki

.

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