Re: abundance of irrationals!)

Virgil said:
> In article <MPG.1ceebe24aa5f40da989c4a@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>
> > Virgil said:
> > > In article <MPG.1ceea26191d35d66989c38@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > >
> > > > guenther vonKnakspot said:
> > > > > aeo6 Tony Orlow wrote:
> > > > >
> > > > > <snip>
> > > > >
> > > > > > Smiles,
> > > > > >
> > > > > > Tony
> > > > >
> > > > > Pray tell us Orlow what is an infinite element of N? That is, what is
> > > > > an infinite number ? And don't confuse that with an infinite amount.
> > > > >
> > > > > Regards
> > > > >
> > > > >
> > > > You mean an infinitely long number, with an infinite number of digits. I
> > > > assume
> > > > that's what you mean, without context.
> > >
> > >
> > >
> > > Since it is only Orlow who insists that any such thing exists, why does
> > > he have no explanation of what HE is taking about?
> > >
> > > And what is the smallest of the natural numbers "with an infinite number
> > > of digits" or otherwise being infinite, Tony?
>
>
> > I said weeks ago that there is no largest finite, nor is there a
> > smallest infinite, by the perspective of counting. That void cannot
> > be counted through. Since you ask for whole numbers, counting seems
> > to be the natural way to ensure wholeness, and therefore I cannot see
> > that there is a smallest infinte natural or largest finite natural.
>
> The let us form the set of finite naturals, and call it S.
>
> Clearly 1 is in S and clearly if n is in S then n+1 is in S, so S
> contains every natural one can get to by finite counting.
>
> Lets do away with N and work only with S.
>
> Have we lost anything important? Not by me!
>
> So that henceforth , my N is the set of FINITE naturals.
>
> If TO wants to include anything else, he must find a new name for his
> set.
>
I already said you can have your set of finite counting numbers. Just don't
claim the set has an infinite number of members unless you can come up with
some infinite set of symbols to represent them. S^L is finite for finite S and
L, period.
--
Smiles,

Tony
.

Relevant Pages

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  • Re: Logarithm of transfinite numbers
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  • Re: infinity
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