Date: Dec 7, 2012 12:24 AM
Author: Virgil
Subject: Re: Cantor's first proof in DETAILS

In article 
<97829085-9b08-479c-b693-fde704b4ffbf@nl3g2000pbc.googlegroups.com>,
"Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:

> On Dec 5, 9:05 pm, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <5312c40d-7490-4838-b49c-573a9f2e1...@i2g2000pbi.googlegroups.com>,
> >  "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:
> >

> > > On Dec 4, 1:15 pm, Virgil <vir...@ligriv.com> wrote:
> > > > In article
> > > > <42cabcca-089d-456f-837a-c1d789bda...@jj5g2000pbc.googlegroups.com>,
> > > > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:

> >
> > > > > And Heaviside's step is continuous,
> > > > > now. For that matter it's a real function.

> >
> > > > I already said that the step function is a real function, I only
> > > > objected to your claim that it was a continuous function.
> > > > --

> >
> > > Heh, then you said it wasn't, quite vociferously
> >
> > I objected to it being called continuous. possibly vociferously, but
> > your claim that it was continuous deserved vociferous objection.
> >
> > :  you were wrong
> >  Don't you wish!
> >
> > , and
> >

> > > within the course of a few posts wrote totally opposite things.  Your
> > > memory fails and that's generous, not to mention you appear unable to
> > > read three posts back.

> >
> > > And everybody sees that.
> >
> > > Then as noted Heaviside's step, a real function, can be simply drawn
> > > classically: without lifting the pencil.

> >
> > Not outside of Rossiana.
> >
> > http://en.wikipedia.org/wiki/Heaviside_step_function
> > The Heaviside step function, or the unit step function, usually denoted
> > by H (but sometimes u or ?), is a discontinuous function whose value is
> > zero for negative argument and one for positive argument. It seldom
> > matters what value is used for H(0), since H is mostly used as a
> > distribution.
> >
> >   It's continuous that way.
> >
> > Not according to Wiki, whom EVERONE here, except possibly WM, trusts far
> > more than they trust Ross.
> >
> > See that phase  "discontinuous function"?
> >
> > Or maybe your as blind as you are thick.
> > --

>
>
> http://en.wikipedia.org/wiki/Heaviside_step_function

From wiki:
The Heaviside step function, or the unit step function, usually denoted
by H (but sometimes u or ?), is a DISCONTINUOUS function whose value is
zero for negative argument and one for positive argument. It seldom
matters what value is used for H(0), since H is mostly used as a
distribution. Some common choices can be seen below.
>
> * ''H''(0) can take the values zero through one as a removal of the
> point discontinuity, preserving and connecting the neighborhoods of
> the limits from the right and left, and preserving rotational symmetry
> about (0,½).


Except that the value of the Heaviside step function AT zero cannot be
chosen so as to make its limit as x increases towards zero though
negative values become equal to the limit as x decreases through
positive values towards zero, which would be necessary to make the
function continuous at zero according to every standard definition of
continuity.

One wonders whether Ross knows what continuity reall is all about.
>
> http://en.wikipedia.org/wiki/Oliver_Heaviside
>
> Looks good to me.


Try getting your eyes tested, and if that doesn't clear things up, get
your brain tested.
--