```Date: Dec 9, 2012 9:26 PM
Author: Virgil
Subject: Re: Cantor's first proof in DETAILS

In article <58d11bea-4bbc-4717-98fc-ca05fa2ce26b@y5g2000pbi.googlegroups.com>, "Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:> On Dec 9, 2:47 pm, Virgil <vir...@ligriv.com> wrote:> > In article> > <ec1e904c-767e-44fa-a13e-21e38f605...@jj5g2000pbc.googlegroups.com>,> >  "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:> >> > > What you missed was that I agreed that, given the definition of> > > "continuous" as being right- and left-continuous at each point and> > > with the same limit, that H-connected is "naturally continuous".  I> > > don't claim that function has properties it doesn't.  It's the straw-> > > man.> >> > Then it is your straw man.> >> > Since you failed to demonstrate that being "naturally continuous"> > differs in your mind, or anyone else's, from naturally being> > "continuous", it is you who are in the wrong here, intending to deceive.> >> > And you also failed to give any definition of being "naturally> > continuous", or any reason to suspect that it had its own meaning.> >> > So I repeat, your original claim of continuity was wrong, and until yo> > provide your definition of "naturally continuous", you claim of a> > discontinuous function being  "naturally continuous" is still not> > exanblished.> > --> > Shoo, fly.> > "There's no gap in this Heaviside step with connecting H(0+) and> H(0-)> with a simple line segment.  There is no point in it such that, not> in> the function, it is the only point in all neighborhoods of any [1]> two> points in the function, not in the function (not even a point> discontinuity).  Here "in the function" is each (x,y) in the combined> coordinate image or co-range, with the function defined by the points> in it.  The two points are from: the left and right limit> sequences,and> the points on the asymptote.  (The contrapositive is a strong> rationale not all find.) "  ([1] of every)> > That one's mine: a definition of continuity.  I'd well surmise it's> already found, but, I discovered it.> > However again as noted, though, you're barking up Euler's and Hardy's> trees, who we hold in high esteem and of authority.  Hardy's> apologetics as noted above may help, as his treatise was the text.> Euler and Hardy give definitions of "naturally continuous", for what> we know that is yet, somewhat, under-defined, reflected in the> "natural" as being "fundamental", "defining", or "primary".> > And then, no, I'm quite against any "attempt to deceive":  quite.> > Hancher, I think you should give our readers somewhat more credit in> terms of their rational ability, else, they give you less.  I give them a good deal more than I give you.--
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