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Re: Matheology § 038
Posted:
Jun 14, 2012 4:46 PM
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On 14 Jun., 22:06, Uergil <Uer...@uer.net> wrote:
> In article
> <d0a7a17e-ef84-4209-811f-544f53222...@w24g2000vby.googlegroups.com>,
>
> WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 14 Jun., 13:56, Gus Gassmann
>
> > > lim(int f_n) =/= int(lim f_n).
>
> > > Ask him to reconcile that with his world view.
>
> > Don't forget, there is one important exception:
>
> > lim(card(q_1, q_2, q_3, ..., q_n)) = card(lim(q_1, q_2, q_3, ...,
> > q_n))
>
> Whether 'card(q_1, q_2, q_3, ..., q_n)'
> or 'lim(q_1, q_2, q_3, ...,q_n)'
> even exist depends on what the q_1, q_2, q_3, ...,q_n are,
> and I see no reason to suppose that they must both exist or both
> non-exist for the sane set of q_i.
>
> So it requires a proof, which is not provided, even to claim that WM's
> proposed equation makes any sense at all.
That proof is required but not given. Nevertheless Cantor "counts" the
rational numbers by equating
lim(card(q_1, q_2, q_3, ..., q_n)) = card(lim(q_1, q_2, q_3, ...,
q_n))
card(q_1, q_2, q_3, ..., q_n) = n
lim n = aleph_0
lim(q_1, q_2, q_3, ..., q_n) = |Q
card(|Q) is something, but certainly not aleph_0.
Regards, WM
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