Re: infinity

In article <MPG.1da71ddbc671b2c398a3ee@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

> Randy Poe said:
> >
> > Tony Orlow wrote:
> > > Randy Poe said:
> > > >
> > > > Tony Orlow wrote:
> > > > > Matt Gutting said:
> > > > > Is there an end to the "endless" sequence of points on the real
> > > > > number line in
> > > > > [0,1]?
> > > >
> > > > No.
> > > >
> > > > > 0.........................1
> > > >
> > > > There is an upper limit to the set of points. But you will never
> > > > get there on any sequence that purports to contain every element
> > > > of the set.
> > > Certainly not in any finite number of iterations.
> > > >
> > > > > I see a beginning and an end to that infinite sequence of
> > > > > infinitesimal points.
> > > > > Am I imagining something?
> > > >
> > > > Yes. You are imagining that the points in between can be listed
> > > > in sequence.
> > > What if they can?
> >
> > They can't.
> Can, too.
> >
> > > 0.000...000,0.000...001,0.000...010,0.000...011,....
> >
> > If those first two strings represent real numbers, then there
> > exists a real number between them. So your list already
> > has a gap in it.
> >
> > - Randy
> >
> >
> I can use sub-infinitesimals,

As there are no infinitesimals to "sub", TO is merely dreaming of
non-existent fractional parts of the non-existent.



> If I declare that there are enough digits in these numbers to denote every
> point in the line segment

There are enough digits, a Dedeking infinity of them, in standard
decimals to represent every point in (-oo,+oo) with some being
represented twice.

Since there are no strings of digits with infinitley many digits between
any two digits, TO's alledged "representations" are unreal fantasies
outside TOmatics.
.

Relevant Pages

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  • Re: crank crank crank
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  • Re: crank crank crank
    ... but he won't accept AP's infinitesimals due to ...  > AP, or anyone else can possibly give, for the ellipsis ... digits is not a number. ... indexed by hyperreals from 0 to -are zero. ...
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  • Re: .9 repeating
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  • Re: abundance of irrationals!)
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