On 2/7/2013 1:54 AM, WM wrote: > On 7 Feb., 08:15, fom <fomJ...@nyms.net> wrote: >> On 2/7/2013 12:45 AM, WM wrote: > >>> For every n: (a_n1, a_n2, ..., a_nn) =/= (d_1, d_2, ..., d_n). >>> For every n: (a_n1, a_n2, ..., a_nn) is terminating. >>> For every n: (d_1, d_2, ..., d_n) is terminating. >> >>> For all n: (a_n1, a_n2, ..., a_nn) =/= (d_1, d_2, ..., d_n). >>> For all n: (a_n1, a_n2, ..., a_nn) is terminating. >>> For all n: (d_1, d_2, ..., d_n) is *not* terminating. > >> that the irrational number, in virtue of >> the property given to it by the definitions >> has just as definite a reality in our minds >> as the rational numbers or even the integers, >> and that one does not even need to gain it >> through a limiting process, but by possession >> of it one becomes convinced of the practicability >> and evidence of limiting processes in >> general." >> >> Notice the word DEFINITION in Cantor's >> statement. > > Definition or not - all cases have to be treated similarly:
Sadly, no one is yet properly treating your case.
> "for all" > either expresses a limit or not.
It does. It is simply not characterized properly by WMorons
> There is not a bit of logic in > arbitrary choice.
You mean there is not a bit of logic in your choices.
