On 18 Apr., 08:52, fom <fomJ...@nyms.net> wrote: > On 4/18/2013 1:42 AM, WM wrote: > > > On 18 Apr., 08:19, fom <fomJ...@nyms.net> wrote: > > >> In constrast to > >> Brouwer, he repeatedly states > >> that there is absolutely no > >> completed infinity. > > > Brouwer also states that. Brouwer accepts infinite sequences that can > > be defined by a finite definition like 0.111... Why the finite > > definition? because there is no chance to get an actually infinite > > chain of symbols 1 (or any other period). > > Brouwer speaks of rule-governed > endless process.
And in contrast to matheologians he knows that a rule is a finite definition. > > The Russian constructivists represent > that with algorithms.
Finite, anyhow. > > WM does not know what a mathematical > rule-governed process is.
Divide 1 by 9, then you have an example probably easy enough for you to understand.
> According to Brouwerian intuitionistic reasoning, > when WM's construction reaches the point where > the sequence of triangular numbers exceeds the > ultrafinitist limit, the contradiction nullifies > the construction.
But not according to potential infinity. On the other hand, it is clear that there is no number with 20 digits on a pocket calculator. In MatheRealism there is no largest number but a largest komplexity of number definitions. > > This is WM's model of mathematics: