Re: Cantor and the binary tree

Virgil said:
> In article <1117019416.558035.49530@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> mueckenh@xxxxxxxxxxxxxxxxx wrote:
>
> A number
> > 0.333... is always equal to a rational with a denominator that is a
> > power of ten. It is simply impossible to assume that this number
> > becomes 1/3. Or is there any occult advantage of the decimal system
> > over the binary system?
>
> That "number" does not have to BECOME 1/3, it already is 1/3.
>
> If one regards 0.333... not as a number but only as a sequence of
> partial sums, it is true that none of those partial sums is exactly 1/3,
> but the mathematical standard for interpreting a repeating decimal, like
> 0.333..., is that it represents that NUMBER which is the limit of that
> sequence of partial sums. And that number, by every reasonable analysis,
> is exactly and precisely 1/3.
>
> WM must be off his meds again.
>
But, Virgil, how do you know that, when you can never get to infinity? Don't
you have to perform all your partial sums? Isn't a limit something that never
gets there? Can you just "jump" to infinity, and declare that infinite set of
partial sums equal to some fraction? It almost sounds like you're coming to
your senses! It's about time!
--
Smiles,

Tony
.