```Date: Mar 6, 2013 1:44 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 6 Mrz., 13:18, William Hughes <wpihug...@gmail.com> wrote:> On Mar 6, 12:48 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > On 6 Mrz., 12:05, William Hughes <wpihug...@gmail.com> wrote:>> > > > L_m is a single line if m is a natural number.> > > > Would you prefer to call L_m infinitely many lines?>> > > Nope, I would prefer to call L_m a function> > > (of time and person).  A function may have as> > > value a "single line of the list"> > > but calling something that changes a "single line of the> > > list" is silly.->> > I said always that L_m is a function (of several arguments) and that> > this function takes as vaules lines of the list. As it takes single> > lines, I don't see why we should not call them single lines.>> Because calling L_m a single line> is certain to cause miscommunication> and using language in a way certain> to cause miscommunication is silly.No. L_m is a single line. You have misunderstood as becomes clear fromthe following.>> So the statement>> "there is no line  which contains every> FIS of d">> becomes in the language of Wokenmuekenheim>> "there is no findable line which contains> every FIS of d">> Similarly, there is no statement about> the behaviour of "actually infinite"> sets that does not have an analogue> in the language of Wolkenmuekenheim.>> For example:>> in Wolkenmuekenheim you would say> (about potentially infinite sets)>>    A subset K of the lines of L>    contains every FIS of d iff>    K has no findable last line.No, it is exactly false to require an infinite subset K to containevery subset of d. Every FIS of d is always in one single line. Thisline is always the last line. Every other line is not necessary andnot sufficient to contain every FIS of d. Without a last line we canprove that no line is sufficient and necessary to contain every FIS ofd.This again testifies that you have not understood yet the nature ofpotential infinity.>> to mean the same thing as the> statement (about "actually infinite sets")>>    A set of lines K contains>    every FIS of the diagonal>    iff K has infinite cardinalityThat is actual infinity and as such different from the former. And, bythe way, the claim is nonsense, since, even in actual infinity, forevery element of K we can prove, that it does not belong to the set oflines necessary or sufficient to contain every element of d.>> This is what I mean when I say> that "potential infinity" behaves> like "actual infinity".So you have not yet comprehenden the nature of potential infinity.It is ridiculous to see how many matheologians claim that a set K thatcontains every FIS of d although it is clear that none of its FIS cansatisfy this claim.Everey line of the complete list11, 21, 2, 3...is not containing the actually infinite set |N.It is claimed that the union does.But this list is constructed such that the union is the same as thesequence.And the limit |N does not belong to the sequence.Therefore it does not belong to the union.Regards, WM
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