```Date: Mar 21, 2013 3:23 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 21 Mrz., 03:41, Virgil <vir...@ligriv.com> wrote:>> > A needed number of lines has a first element.>> Nope!>> Any sufficient set of lines will have a first element, but as there are> pairs of such sufficient sets which are disjoint, there is no first> element common to all sufficient sets.I am not interested in sufficient sets but in necessary sets.>> > If lines were chosen, that are superfluous, they cannot belong to the> > needed number.>> The number of lines needed is infinite, but there are infinitely many> pairwise disjoint setseach of which contains only unnecessary lines. At least hithertonobody has succeeded in naming a necessary line. Every named neededset starts with a not needed number.> If the sets are pairwise disjoint, thenthen the intersection of them is empty.How can they all contain the complete set of natural numbers in thiscase?And if at least two of these sets contain |N, how can they bedisjoint?>>>> > > A set of needed lines exists.>> > Name the frist line. Or confess that not every set of natural numbers> > is a set if natural numbers that obeys the rules established in set> > theory for sets of natural numbers.>> That first sentence is not English.>> That second sentence does not scan in ENglish eoither..What is eoither? Here my dictionary fails.>>>> > > A set of necessary lines does not.->> > Ah, a needed line is not a necessary line?>> No particular line is needed as long as some subsequent line is included.What is the first one?I can prove by induction, that there is no necessary subsequent line,except a / the last one.It is a pity. You and your ilk are unable to apply induction, butboast of  of "transfinite induction". Note: Transfinite induction canbe applied to show that its applyer is a fool that should be inside amad-house. Further merits of transfinite induction are not known.Regards, WM
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