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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