Re: induction vs Cantor

From: Virgil (ITSnetNOTcom#virgil_at_COMCAST.com)
Date: 12/03/04 

Date: Fri, 03 Dec 2004 01:10:37 -0700

In article <mrRrd.107123$T02.45547@twister.rdc-kc.rr.com>,
 "Poker Joker" <Poker@wi.rr.com> wrote:

> "Virgil" <ITSnetNOTcom#virgil@COMCAST.com> wrote in message
> news:ITSnetNOTcom%23virgil-F79602.12115927112004@[63.218.45.211]...
> > In article <WG1qd.94256$T02.42752@twister.rdc-kc.rr.com>,
> > "Poker Joker" <Poker@wi.rr.com> wrote:
> >
> >> "Virgil" <ITSnetNOTcom#virgil@COMCAST.com> wrote in message
> >> news:ITSnetNOTcom%23virgil-73DFB8.22294326112004@[63.218.45.211]...
> >>
> >> > <snipped>
> >>
> >> > What I am saying is that if one can consider the totality of all
> >> > functions from N to R, without worrying about constructability, then
> >> > there is no problem with the "diagonal" proof of Cantor's theorem,
> >> > since
> >> > the Cantor anti-diagonal algorithm applied to any member of that set of
> >> > functions is guaranteed to produce a number not in the image of the
> >> > function, and that production is what I have called the Cantor function
> >> > from R^N to R.
> >>
> >> Uses Cantor's conclusions.
> >
> > No. Only his assumptions.
>
> No. His conclusions.

Which ones? Are Cantor's conclusions about the value of 1+1 to be
excluded as well as his conclusions about the uncountablity of reals?

Is anything that tends to lead ultimately to the uncountablility of the
reals to be excluded?

Uncountability is nowhere a rerequisite of the construction of what I
have called the Cantor function, it is only a consequence of it, so it
seems to me that you are outtlawing anything leading to Cantor's
conclusion, not merely the conclusion itself.

It is not clear to me that your blanket accusation does not rule out
even 1+1 = 2, unless you are a bit clearer about just which
"conclusions" are to be outlawed.

Relevant Pages

  • Re: how to list all of the real numbers
    ... Some of the reals ... I have the impression that Calvin is earnestly learning about ... uncountablity and such, and he is sharing his ways of thinking about the ... The topic of uncountability is so often brought up by cranks that it is ...
    (sci.math)
  • Re: induction vs Cantor
    ... excluded as well as his conclusions about the uncountablity of reals? ... It is not clear to me that your blanket accusation does not rule out ...
    (sci.math)
  • Re: how to list all of the real numbers
    ... If you read Calvin's original post, his real numbers are represented by *paths* in a binary tree. ... Some of the reals ... I have the impression that Calvin is earnestly learning about uncountablity and such, and he is sharing his ways of thinking about the issue. ... He does not strike me as a crank who, for example, insists that the reals must be countable. ...
    (sci.math)
Loading