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

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: WMytheology � 293
Posted: Jun 24, 2013 3:13 PM

mueckenh@rz.fh-augsburg.de wrote:

> On Sunday, 23 June 2013 23:05:45 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.
>
> 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.

Outside of WMytheology, (F(n) U F(n-1) U ... U F(1)) = F(n)

so Rest(n) = "|N\Fison(n)"!

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,
even in WM's wild weird world of WMytheology.
--