Date: Mar 21, 2013 3:03 PM
Subject: Re: Matheology � 224
On 3/21/2013 5:21 AM, WM wrote:In article
> fom <fomJUNK@nyms.net> 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?
That falsely presumes what was not asserted.
Namely, that stating that one can do something with any finite set of
lines does automatically requires or implies that one cannot do it with
infinite sets o lines.
And in this case, one can also do it with some , but not all, infinite
sets of lines from the original set.
Given an infinite, and therefore sufficient, set of lines covering |N,
one can remove any subset which does not leave a finite residue and that
infinite residue will still cover |N.
Thus one CAN remove SOME infinite subsets of the original and still
cover |N, contrary to WM's false and unwarranted presumption.