Re: Is continuum completely filled up?

• From: Tony Orlow <tony@xxxxxxxxxxxxx>
• Date: Sun, 07 Jan 2007 19:11:14 -0500

"Saurav" <saurav1b@xxxxxxxxx> wrote in message
news:1167459989.569012.274570@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

ooo wrote:

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.

First, I would advise you to use something considerable in the place of
nickname. "ooo" looks quite odd! Change it, please.
I tell you, when I started to read mathematics of the real line, such
questions came into my mind; and I used that time to think about the
possible meanings of "next number". Why there is no gaps in real line
ruffled my mind. But as it has made the whole scenario clear, step by
step, through myriads of misconceptions and corrections, I am sure that
you also will understand what is meant by "gaps" and why completeness
is contrary to gaps.
I advise you to nurse your questions in mind; and ask others, as you
did, and if not satisfied with their answers, keep on reading....to
realize what the resl line looks like shall need years; many properties
of it, topological, measure theoritical, set theoritical ...are there,
without knowing which you can not possibly afford to a clear picture of
the real line.
I recommend a book : Hobson's book, "The thory of functions of a real
variable and the theory of Fourier's series". After you have had a
priliminary understanding of the structure of R, you should read this
book.

The question of wheather real line is filled up or not is the same as the
question that
1.wheather all space is filled up, (or zeno's paradox achilles and
tortouse)
2.or motion of rotating disk is completed
3.throughing dice is completed
expression might be uncomprehencible.
1.

• References:
  • Re: Is continuum completely filled up?
    • From: ooo

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