```Date: Mar 24, 2013 5:07 PM
Author: ross.finlayson@gmail.com
Subject: Re: Matheology § 224

On Mar 24, 1:44 pm, "Ross A. Finlayson" <ross.finlay...@gmail.com>wrote:> On Mar 24, 12:22 pm, Virgil <vir...@ligriv.com> wrote:>>>>>>>>>> > In article> > <d28c00b4-cbad-4067-a2b1-cf63a83f9...@g4g2000yqd.googlegroups.com>,>> >  WM <mueck...@rz.fh-augsburg.de> wrote:> > > On 24 Mrz., 03:01, Virgil <vir...@ligriv.com> wrote:>> > > > > In set theory we can construct the set of all elements that have a> > > > > certain property. Does that mean that the property vanishes if too> > > > > many elements belong to the set?>> > > > It only vanishes from among non-members of that set.>> > > Correct. But here I use only members, namely FISONs.>> > > If you subtract a finite number from an infinite number, nothing> > > happens.>> > > If we remove a finite line from our list>> > > 1> > > 1,2> > > 1,2,3> > > ...>> > > the union of all lines is not changed.>> > Except that that list, which does not have a last member, cannot be one> > of WM's lists. which are all required to have a last, though evanescent,> > member.>> > > We can even repeat this procedure for an infinite number of times>> > Not in Wolkenmuekenheim, in which nothing can be done infinitely many> > times, even theoretically, so Zemo's [sic] riddles prevent all motion there.>> Are you saying that lim_n->oo Sum_i=1^n 1/2^i =/= 1, or, that> Sum_i=1^oo 1/2^i = 1?>> Then, where the lines are n-sets:  what is the union of the lines?> Via induction, any element of N is in line n and all following.  There> does not exist n e N s.t. not exists m>n-set contains n, and for all m> n.  If the union of the lines is not a line, then only the union of>> finitely many lines is a line, transfer doesn't hold.  Yet, there are,> or aren't, infinitely many lines.>> Basically this gets into the difference between the _definition_  of> successor (axiomatization), and successor as a _structural> consequence_, of variety (deduction).>> The sum of all the finite numbers (natural integers): isn't a finite> number, and for no finite number is it their sum.  Yet, addition is a> closed operation in the integers.  That gets into the difference> between operations that are closed for finitely many, and unboundedly> many, and infinitely many applications of the operation, here> addition.  The transfer principle, that which is so for each is so for> all, can be further refined to bounded and infinite transfer.  And, it> should be.  Then there is reasoning as to separate the notions of the> quantifiers for each / for any / for every / for all into various> categorizations of application, that the "universal" quantifier> correctly reflects the existence of transfer.>> Then, just as there are Euclidean and non-Euclidean geometries of> reasonable import, there are Archimedean and non-Archimedean natural> integers, not just potential and complete, but along those lines.>> In the consideration of the application of the operations, and Mazur's> swindle as it were or the well known result of 1-1+1-1..., in the> telescopic it is seen that addition and its complement as subtraction,> is finite-closed and bounded-closed, and may be infinite-closed, _for> the range of the inputs_, that the set isn't just defined by its> elements, _but all operations contingent upon it_.  And, for some> collections, their elements are defined by their access, here the> continuum of real numbers: sensitive in their ordering.>> Then, where the limit is the sum, or regardless of that and the limit> exists, EF sweeps [0,1], BT the CIBT, the list as 0, 1, 2, ...,> prefixed by the radix:  has for the only element different from each,> that each is only different from each other.>> To each their own.  And, all for one and one for all, as it were.>It is much as the consideration of convergence (rel. divergence), hereof the convergent series or infinite product.  Addition is closed forthe convergent series to exist.  It only need be bounded-closed forthe standard results to hold.  Yet, the limit, _is_ the sum, else, thesum is partitioned into its pieces, again the limit _is_ the sum, aswe know Zeno's arrow arrives.  Here, then in what today we call asingle reference frame, Zeno's arrows arrive because _all_ of themarrive.  Arithmetical scalar properties of non-zero convergent seriesexist because they share the free variable.Can't have a diagonal without a square.Regards,Ross Finlayson
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