Date: Mar 21, 2013 2:59 PM
Subject: Re: Matheology § 224
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:
>>>> 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
Claims are easy. The mathematics to back such
claims is not. Your readers await your justification
for this statement without appeal to completed infinity.