Re: Cantor and the binary tree

In article <MPG.1cfe8e078fe6cf0c989d29@xxxxxxxxxxxxxxxxxxxxxxxxx> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> Virgil said:
....
> > 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.
....
> But, Virgil, how do you know that, when you can never get to infinity? Don't
> you have to perform all your partial sums?

No.

> Isn't a limit something that never
> gets there?

Indeed.

> Can you just "jump" to infinity, and declare that infinite set of
> partial sums equal to some fraction?

No, apart from the use of the word "set" in this context.

A limit is defined using finite sums only.
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