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"Saurav" <saurav1b@xxxxxxxxx> wrote in message
news:1167570442.876679.285710@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>
> ooo wrote:
> > "Robert Maas, see http://tinyurl.com/uh3t"; <rem642b@xxxxxxxxx> wrote in
> > message news:REM-2006dec30-001@xxxxxxxxxxxx
> > > > From: "ooo" <fara...@xxxxxxxxx>
> > > > If real line is filled with points and each point is
> > > > distinguished,then each point has difference from every other
> > > > points.
> > >
> > > Yes, however the difference from a given point to various other
> > > points can be arbitrarily small (close to zero).
> > > Between a given point and any other point on one side of it, there
> > > are lots and lots of other points.
> > Then all reals cannot be listed (I don't now apropreate words,but I
don't
> > mean reals is numbered, but rather cannot complehend. )
> > If there are nowhere to be listed all reals in anyform,where they exist
,on
> > real line? But we cannot take up all of them as a form we can deal with
from
> > there.
> > > But there is no single place that is between a given point and all
> > > other points on one side of it.
> > >
> > > > Therfore real line has void.
> > >
> > > Nope. Anywhere between real points you think there's a void, in
> > > fact there's at least one real point in there to refute your void.
> > >
> > > It gets more interesting if you talk about voids between sets of
> > > real points instead of between two singleton real points. Given any
> > > two sets, where all the points of one are strictly less than all
> > > the points of the second set, there is at least one real point
> > > "between" the two sets in the sense that it is either:
> > > - The very greatest element of the set of lesser points.
> > > - The very least element of the set of greater points.
> > > - Strictly between the two sets.
> > Abobe explanation is similler to a case that berween any two reals
,there
> > exist at least one real ,even though not so much .
> > Please cosider follouing question I intended to posr another place.
> > These arguments ,including Cantor's diagonal, mention up to countable
> > case,and assume that these argument hold for infinite numbers objects.
> > These arguments sometimes lead to confusion.
> Cantor's diagonal argument shows that the real numbers are not
> countable; where we mean by the statement "A is countable" that there
> is a one-to-one correspondence, that is, a bijection, between the set
> of natural numbers and A.
> > In the question of vase and ball, argument is
> > cardinarity of all added balls and that of removed balles is equevalent,
> > hence at noon number of ball is 0 on the vase regardless process
before
> > then.
> > Is it not the same with that cardinality of all naturas is equevalent
with
> > that of even numbers, so that naturals minus even numbers = 0.
> > Why can it be ?
> I can't understand what you have tried to mean. There are as many
> naturals as the even ones are.
> You seem to be a bit inefficient in English; it is no crime; we all
> non-Englishmen have some lapse in our knowledge of English; in fact, I
> am not an Englishman, and I ->do<- write wrong English, but it is not,
> as you have mentioned, what I intend. If you are not sure whether what
> you write is lucid, use mathematical notations as much as possible.
> The correspondence : n |--------> 2n is a bijection between the
> naturals and the even naturals.
> >
Thank you for your kind advice. I shall explane my statement above later.
My new name may be effective for post I received after 2006/12/31.
Regards OT
>
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