Re: Cantor Confusion

In article <452e5a9d@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Randy Poe wrote:
Tony Orlow wrote:
*** T. Winter wrote:
In article <1160551520.221069.224390@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
"Albrecht" <albstorz@xxxxxx> writes:
> David Marcus schrieb:
...
> > I don't follow. How do you know that the procedure that you gave
> > actually "defines/constructs" a natural number d? It seems that you
> > keep
> > adding more and more digits to the number that you are constructing.
>
> What is the difference to the diagonal argument by Cantor?

That a (to the right after a decimal point) infinite string of decimal
digits defines a real number, but that a (to the left) infinite string
of decimal digits does not define a natural number.
It defines something.

But not necessarily a number.

What do you call that? If the value up to and
including every digit is finite, how can the string represetn anything
but a finite value?

Because representations of finite values end, and the string doesn't
end, so it breaks the rules of "strings that represent finite values".

- Randy


Can you rightly call it an infinite value? I can't. It's unbounded like
the finites themselves, but not infinite, as long as all digit positions
are finite.

Then is TO claiming that the infinite binary string ...111 represents a
finite natural? Note that all digit positions in ...111 are finite.
.

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