On Friday, 20 December 2013 17:44:36 UTC+1, wpih...@gmail.com wrote: > On Friday, December 20, 2013 12:14:11 PM UTC-4, muec...@rz.fh-augsburg.de wrote: > > > > > > >the number of finite formulas is countable.
in set theory. > > > > The finite formulas that produce 0/1 sequences *are* > > the potentially infinite 0/1 sequences.
No. Counterexample: The potentially infinite sequence of 1's is given by many finite formulas like 1/9 or "0.111..." or "the potentially infinite sequence of 1's behind the point", which are not the sequence but determine the sequence: The finite formulas allow to calculate every digit and the limit, if existing.
> There is no > > list of the potentially infinite 0/1 sequences, thus > > there is no list of finite formulas.
In potential infinity there is nothing infinite finished. There is no list of all finite formulas, there is no list of all sequences.
> Note that this > > conclusion was reached without recourse to "actual infinity". > > If there is a contradiction it is a contradiction with > > "potential infinity".
What kind of contradiction are you alluding to? Potential infinity is unfinished infinity. That is not a very new aspect.