On 22 Mrz., 10:49, fom <fomJ...@nyms.net> wrote: > On 3/22/2013 4:13 AM, WM wrote: > > > On 22 Mrz., 09:54, Virgil <vir...@ligriv.com> wrote: > >> On 3/22/2013 1:38 AM, WM wrote: > > >>> This proves that we can remove all finite lines from the > >>> list without changing the contents of the remaining list. And this is > >>> remarkable, isn't it? > > >> Since WM also claims that all the lines of that list are finite lines, > >> WM is now claiming one can trow out the entire contents of a list and > >> still have the entire original list in place. > > > That is a consequence of the completed infinity of set theory. > > He is referring to your claims
I know. They are a consequence of finihed infinity. > > > >> Unfortunately, as in the above claim, what WM claims to be the case > > > can be proven by induction that holds for every finite line. > > Every number that belongs to line n belongs to the next lines too. > > It should be observed, once again, that the most WM is ever referring > to with statements like this is the form of the domain for an > induction rather than any true use of inductive proof.
True use of inductive proof has been fonuded by Fermat without any reference to domain. Your "true use" refers to "the only method you have been taught". > > > If you are of different opinion, please name a finite line that is not > > covered by induction. > > Since iterated concatenation as a definition of number > is not induction,