Re: Is continuum completely filled up?

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

.

Relevant Pages

  • Re: How Many Of You Had To Teach Yourself The Math?
    ... using derivatives. ... bottom lid) and body cylinder itself that must be made out of the ... this point, we have two variables, H and D, and there are an infinite ... One where the area of the lids is about zero and the ...
    (sci.electronics.basics)
  • Re: TM Tape is Always Finite
    ... process to be repeated an infinite number of times; ... mental model of infinity, and has tripped you up at least ... one that holds for that zero for all time. ... > to assume that TM2 can as well. ...
    (comp.theory)
  • Re: An infinite number question
    ... If you exclude 0, the remaining numbers form a group ... A set with both addition and multiplication is a ring, ... If the set is a cyclic group under addition, as would be the infinite ... division except by zero is possible. ...
    (talk.origins)
  • Re: Interesting math
    ... notion established by centuries' worth of mathematicians and others. ... Zero is both odd and even. ... an infinite number set, positive and negative. ... one with the cardinality of the reals, ...
    (alt.usage.english)
  • Re: Is a line segment composed of points?
    ... piece if of zero length, then it is not a result of cutting at ... You end up with an infinite number of pieces, ... segment is a matter of how you define line segment. ... first segment is not reached by a division process. ...
    (sci.math)
Loading