The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Matheology § 233
Replies: 20   Last Post: Apr 4, 2013 10:16 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 8,833
Registered: 1/6/11
Re: Matheology � 233
Posted: Apr 2, 2013 5:46 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article
WM <> wrote:

> On 2 Apr., 02:06, Virgil <> wrote:

> >
> > > Nevertheless Cantor has given a finite formula to construct the list
> > > of all rationals between 0 and 1. From that formula we can find every
> > > entry and the anti-diagonal up to every digit d_n. From that we can
> > > easily prove that for every FIS d_1, d_2, ..., d_n of d there are
> > > infinitely many rationals with the same FISs. For every finite number
> > > n - and there are no other lines than such enumerated with a finite
> > > number!

> >
> > But as there is no end to the set/list of natural/finite numbers, there
> > is also no end to the set/list of such lines.

> What shall that "argument" be good for?

WM is continually claiming a "last" natural must always exist, even
though it is always also indeterminate, but now any of his arguments
that require such a last natural automatically fail.

> Why should there be an end?

That's what we keep asking WM.

> If I say every natural number is divisible by 1 without remainder.
> Would you doubt that on the grounds that there is no end to the
> sequence of natural numbers? Such that possibly a natural number would
> follow that is not divisible by 1?

WM has long been claiming that every and any set of naturals must have
an inaccessible last member, i.e., that every set of naturals is
necessarily a subset of a FISON (finite initial set of naturals),
just as he always claims that in a Complete Infinite Binary Tree every
path is a FISON (finite initial sequence of nodes), but he is wrong on
both counts..

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.