Re: infinity

In article <MPG.1d6d4783f28481f898a0e4@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> stephen@xxxxxxxxxx said:
> > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > > stephen@xxxxxxxxxx said:
> > >> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > >> > Randy Poe said:
> > >> >>
> > >> >> Tony Orlow (aeo6) wrote:
> > >> >> > because you claim there were balls in the vase, and then it became
> > >> >> > empty, and
> > >> >> > you are only removing 1 ball at a time, so there MUST have been a
> > >> >> > last ball
> > >> >> > removed. However, you cannot name that last ball removed, since
> > >> >> > there is always
> > >> >> > another to remove. If you DID name that last ball removed, the I
> > >> >> > can name 9
> > >> >> > times as many as have been removed that have not been removed.
> > >> >> > Don't you feel
> > >> >> > like you are trying so sail a big sponge across the sea? Do you
> > >> >> > wonder why it's
> > >> >> > such a drag?
> > >> >>
> > >> >> Can you name the last point between 0 and 1 which is less than 1?
> > >> >>
> > >> >> - Randy
> > >> >>
> > >> >>
> > >> > Binary 0.111...111
> > >> > Decimal 0.999...999
> > >>
> > >> What is (0.999...999+1)/2? Is it between 0.999...999 and 1?
> > >> Or is it undefined?
> > >>
> > >> Stephen
> > >>
> > > 000...000:000...000.999...999:500...000. Very good. You got half an
> > > infinitesimal out of me! ;D
> > > --
> > > Smiles,
> >
> > > Tony
> >
> > Is it between 0.999...999 and 1? If so, then 0.999...999 is
> > not the last point between 0 and 1 which is less than 1.
> 0.999...999 is the last first-level infinitesimal in the first unit. You have
> just dipped your toe into the second level of infinitesimals.
> >
> > If it is not between 0.999.999 and 1, then where is it?
> That's where it is, in between those two points which you consider identical.
>
> > You are going to have to redo a lot of basic arithmetic
> > as x<y -> x < (x+y)/2 < y is a direct consequence of basic
> > arithmetic.
> That still holds.

Which is larger, and why?
000...001010...000 or 0000...0110...0000 ?
.

Relevant Pages

  • Re: Tetration
    ... Good luck, and thanks. ... Smiles, ... Tony ... Prev by Date: ...
    (sci.math)
  • Re: Tetration
    ... Thanks, and good luck! ... Smiles, ... Tony ... Prev by Date: ...
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  • Re: infinity
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  • Re: a question for the anti-Cantorians
    ... infinity doesn't exist. ... Smiles, ... Tony ... Prev by Date: ...
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  • Re: infinity
    ... >> 0.999...999 is the last first-level infinitesimal in the first unit. ... >> just dipped your toe into the second level of infinitesimals. ... Tony ... Prev by Date: ...
    (sci.math)
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