Date: Dec 4, 2012 1:47 AM
Author: Virgil
Subject: Re: Ross' Delusions re his EF.

In article <dac80fce-8253-4320-aa88-4ce8ebe4029a@b4g2000pby.googlegroups.com>, "Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:> Yes, Dirac's delta as it is:  is extra the standard, encompassing it,> AND beyond it.  (And of course it's rigorously modeled by standard> real functions and relevant to the pure AND applied in mathematics.)If that were really the case, Ross should be able to give a real value of the Dirac delta for any real argument, such as its value at zero.Can you do that, Ross?> And Heaviside's step simply has each value between [-1,1] in y on the> vertical line through the origin.Graphs of real functions in the xy-plane do not have any more than one point on any vertical line, so anything like Heaviside's step which does, cannot be a real function.> > And EF goes to one.  So though none of the _finite_ naturals have that> n/d > eps, for each positive eps < 1 there is an element of the range> y thus that y > eps, or y -/-> 1, as it does:  y = EF(n) -> 1.  So, as> is typical, you didn't complete the statement.Ross claims that there are a sequence of constant functions EF_n(x), 1 for for each n in |N, with domain {1...n} and constant value 1/n.So far so good. But now he also claims a constant function, EF(x), with Domain |N , with EF(m) = EF(N) for all m and n in |N  and such that the sumSigma_( n in |N) EF(n) = 1.Those what are more familiar with standard number systems that Ross appears to be will easily see that this cannot be true in those standard systems>  Would you have that> lim Sum 1/2^n < 2, n e N?  0 e NIrrelevant. Ross has to produce a STANDARD real number, x, such that Sum_(n= 1...oo) x = 1. Note that for every natural number n, 1/10^n is too large to be that x,and lim_(n -> oo) 1/10^n = 0, so Ross' alleged x cannot be any larger than 0, and any number of zeroes, even infinitely many, still adds up to only 0.At least in standard mathematics.But possibly Ross is emulating WM by creating a private world of his own where he can command impossibilities. :  lim Sum_n=0^\infty 1/2^n = 2.  It's> not that there's no smallest n that it is, it's that there's no> largest n that it can't be.> > So, it is false for you to (m)utter that d/d =/= 1, or that your false> challenge applies to any. Your EF function, Ross, would require a real number to exist which is larger than zero but smaller than every positive real number. In any standard model of the reals, such numbers do not exist, so that before Ross can use his EF for anything, he will have to invent a wols new number system in which it can operate witout contradiction.>  It's not a failure to note that your> "challenge" is to confirm a falsehood, nor is it much of a challenge.But it is a lie to note any such thing, since the only falsehood involved is Ross' claim that his EF limit function is compatible with e standard real numbers.If EF were actual, why can't Ross give a decimal or fractional value for EF(1)?> > It's not that there's no smallest n that it is, it's that there's no> largest n that it can't be.> > There are only, and everywhere, elements of the "real" continuum, as> we well know them as real numbers, between zero and one, and so are> those from infinity back to infinity fore, for some including> infinity, and for none including transfinite cardinals nor your> imaginary numbers (which are elements of the Argand plane and in> extension to the hypercomplex).But there is no number between zero and every positive real, which number is what the value of Ross' EF function would have to be if it were to exist.> > No, it is our rules, of the reals.Your rules are not the rules of the real reals, only of your imaginary ones..  And, those are discoveries, not> inventions, for the real, to the concrete, in mathematics, with> rigor.  We are simply curators, not owners, of these eternal truths.Then Ross should be fired for incompetence as he sickens then not cures them.> > And, application already has and uses the projectively extended real> numbers, in mathematics, for, for example, physics.Citations?Recall that Ross claims his EF function, the limit one, has the properties(1) that for all naturals n and m, EF(m) = EF(n), and simultaneosly (2) SUM_(N in |N) EF(n) = 1Now if, for some n, EF(n) > 0, the there is some m in |N such that EF(n) > 1/m. but then SUM_(n = 1..m+1) EF(n) >1,Thus EM(n) = 0 for all n and any sum of EM()s is still 0.The mathematics of the standard set |N and the standard ordered field of reals, |R,  are incompatible with existence of Ross' alleged EF function.--