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Topic: Matheology § 293
Replies: 44   Last Post: Jun 27, 2013 2:25 PM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Matheology § 293
Posted: Jun 26, 2013 10:23 AM

On Monday, 24 June 2013 21:13:32 UTC+2, Virgil wrote:
>>> > If you are ready to swallow that the sequence
(1/|Rest(n)|) = 0, 0, 0, > > > ... "converges" to limit oo,

> > > 1/|Rest(n)| is NAN (Not A Number).

> > aleph_0 is a number in matheology, namely greater than n for every n.
> > Therefore 1/|Rest(n)| is a number, namely 0. At least less than 1.

No objections?

> > If all natural numbers are in FISONs, then no natural number is outside of > every FISON. Since the FISONs are inclusion-monotonic, the natural numbers > cannot be spread over several FISONs. Therefore
Rest(n) = |N \ (F(n) U F(n-1) U ... U F(1)) has the limit { } with cardinality 0.

> (F(n) U F(n-1) U ... U F(1)) = F(n) so Rest(n) = "|N\Fison(n)"!

Of course. That does not invalidate my equation.

> Thus if the limit of your "Rest(n)" is {} then the sequence of FISON(n) must also have a limit and that limit must be all of |N

Of course. Therefore the limit is not existing. The sequence 0,0,0,... has not limit oo. Not in mathematics.

Regards, WM