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

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Posts: 18,076
Registered: 1/29/05
Re: Matheology § 233
Posted: Apr 2, 2013 4:31 PM
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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? Why should there be an end?
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?

Regards, WM

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