On 1 Mai, 17:29, Gus Gassmann <no...@nospam.com> wrote: > On 01/05/2013 9:26 AM, Dan wrote: > > > > > > > On May 1, 2:55 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > >> On 1 Mai, 13:15, Dan <dan.ms.ch...@gmail.com> wrote: > > >>> Do you think the natural numbers *can be enumerated*? > > >> No. Look here for a detailled exposition: > > >>http://arxiv.org/ftp/math/papers/0305/0305310.pdf > > >> Regards, WM > > > If I knew it were possible for 4 to follow 2 in the natural numbers , > > I would be worried to use infinity . The difference between a 'unknown > > infinity' and 'the infinity of natural numbers' , is that the latter > > is determined, by thought , and within thought . There is no bluing, > > no information missing, no indeterminacy . > > 2 is always followed by 3 . > > 999 is always followed by 1000 . > > > If I thought of a formula for an infinite sequence of digits, I can't > > pretend "not to know the digits" , or the formula , when communicating > > with myself . > > > I've honestly tried to follow the argument in section 5 , but it's > > incomprehensible . Honestly , it doesn't matter. > >http://arxiv.org/find/math/1/au:+Mueckenheim_W/0/1/0/all/0/1 > > What should matter, really, is the absence of any collaborative work > > in your efforts . Must be very lonely at the top . > > Give it up, Dan. WM's pons asinorum in the paper is the idea that there > can be (actually) infinitely many integers, each of which is finite.
That's not my idea, but is the assertion of the advocates of actual infinity.
> Since you cannot convince him of this fact, any further discussion is > bound to be fruitless.
Perhaps, someone has an idea how to save matheology even from this argument?
For every natural number n the sequence (10^-1, 10^-2, 10^-3, ..., 10^-n) can be reflected at the decimal point to (10^n, ..., 10^3, 10^2, 10^1).
Obviously this transformation does not depend on the number of terms and does not depend on the number of exponents, but solely on the condition that all exponents are natural numbers.
Now try the sequence for 1/9. The claim is that all exponents are natural numbers too. Has it a complete decimal representation with only natural exponents?