On 3/21/2013 6:51 AM, WM wrote: > On 21 Mrz., 11:36, William Hughes <wpihug...@gmail.com> wrote: >> On Mar 21, 11:21 am, WM <mueck...@rz.fh-augsburg.de> wrote:> On 21 Mrz., 08:57, William Hughes <wpihug...@gmail.com> wrote: >> >> <snip> >> >>>> There is such a thing as a sufficient set of >>>> lines (all sufficient sets are composed >>>> entirely of unnecessary lines, which means >>>> that you can remove any finite set of lines >> >>> Why only finite sets? >> >> You can only use induction to prove >> stuff about finite sets. > > For finite sets induction is not required.
As is apparent from reading Markov, this is not true unless one is assuming a completed infinity.
Markov's characterization of potential feasibility speaks of these matters. In particular, induction arises from 'confidence' in the preliminary construction of cases for small numbers.
So, for unmanageably large finite sets, induction is required.
Claims are easy. The mathematics to back such claims is not. Your readers await your justification for this statement without appeal to completed infinity.