Date: Dec 5, 2012 11:03 PM
Subject: Re: Cantor's first proof in DETAILS
On Dec 4, 1:15 pm, Virgil <vir...@ligriv.com> wrote:
> In article
> "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: you were wrong, 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. It's continuous that way.
And simply, the limit from the left and right is connected to the line
through the origin.
Draw a line: you can't lift the pencil. That's basically what
Cantor's proofs say, of functions from natural integers, to line
segments of the reals. Stippling never fills the line: draw it.
Draw a line without putting down the pencil.
Good luck with that,