
Re: Cantor's first proof in DETAILS
Posted:
Dec 5, 2012 11:03 PM


On Dec 4, 1:15 pm, Virgil <vir...@ligriv.com> wrote: > In article > <42cabcca089d456f837ac1d789bda...@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: 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,
Ross Finlayson

