On 17.03.2025 18:49, FromTheRafters wrote:

on 3/17/2025, WM supposed :

You seem to think that there is N_def followed by a fairy dust of
undefined elements which get left behind after some small sequence of
finite members (FISON) are 'removed' from N (leaving fairy dust
behind as a set) instead of 'constructing' a new set from 'the
elements of' the set of naturals.

So it is! Remember the harmonic series. It is infinite although all
defined numbers are separately collected in converging subseries.

I don't know what you expect to achieve along these lines,

It is simple: All definable digit sequences can be split off. Only dark
terms remain and make the series diverging.

Regards, WM

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