
Re: § 424 Actual Infinity: WM never got it  but we get it!
Posted:
Feb 10, 2014 3:31 AM


Am Montag, 10. Februar 2014 00:15:19 UTC+1 schrieb Virgil: > In article <a60f8f4fd749481aa8b6b8d01334a560@googlegroups.com>, > > WM <wolfgang.mueckenheim@hsaugsburg.de> wrote: > > > > > Am Sonntag, 9. Februar 2014 21:50:37 UTC+1 schrieb Virgil: > > > > > > > > > > > Note that if there were any solitary antidiagonal, there would have to be > > > > > first d_n completing it > > > > > > How can there be a digit completing what has no last digit? > > > > > It cannot be. That's why an infinite string of digits does not determine a > > > real number. > > > > > > That has nothing to do with whether an infinite string of digits can > > determine real number.
It has. Compare § 430 of today. > > > > Given a radix position in that string and a base, every different such > > infinite string corresponds to a different real number.
Not at all. A string of digits does not definbe a number. It is possible to define real numbers that have the asserted strings. But that requires finite definitions. > > > > If WM thinks otherwise, let him present such a string, with specified > > base and radix point, that he claims does NOT represent a real number.
The string 0.59765 does not represent a real number unless you define that only zeros (or any other definable sequence of digits) will follow. That, however, requires a finite definition. > > > > > > > And note that the definition of a number has to have an endsignal. > > > > But any infinite sequence's "end signal" indicates infinitely many terms > > before it takes effect.
Therefore the digits that will follow have to be defined by a finite expression. > > > > > > > > > > > > > > > > The defnition of an infinite sequence doe not require it to have a last > > > > term. > > > > > > The definition _of_ the sequence is finite. That determines a limit. The > > > definition _by_ the terms of the sequnece does not exist. > > > > But definition by the terms of the sequENce dose. >
No.
Regards, WM

