Virgil
Posts:
9,012
Registered:
1/6/11
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Re: Joel David Hamkins on definable real numbers in analysis
Posted:
Jun 28, 2013 3:09 PM
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In article <83c237ac-155b-4ee2-8c68-14d303d57722@googlegroups.com>,
mueckenh@rz.fh-augsburg.de wrote:
> So, you can prove that a collection of finite decimal sequences
> contains an infinite one.
An infinite set of finite sets can have as its union an infinite set
everywhere outside of WNM's matheological messup.
>
> IF: An infinite collection of finite decimal sequences, when written in one
> line, makes an actually infinite collection,
The relative 'orientation' of finite sequences is irrelevant, since
sequences are functions having either a FISON or |N as domain.
If WM wants to concatenate strings instead of sequences, that would at
least be possible without the sort of wild handwaving typifying WM's
mytheology.
> THEN: an infinite collection of finite decimal sequences written in different
> lines does the same.
When one does NOT concatenate the strings in a list of strings, one does
NOT get a single string containing all of them.
> (Unioning over subsets cannot not extend a set.)
Unioning over subsets of a set creates a rand NEW set, at least outside
of WM's wild weird world of WMytheology.
Given only set {{1,2},{3,4}}, one does not have set {1,2,3,4} until one
unions {{1,2},{3,4}} "over its subsets".
>
> >
> > > "For every n there exists k such that a_kn = d_n" is a contradiction for
> > > mathematicians who take the trouble to try to escape it - without success,
> > > of course.
> >
> > That doesn't imply, "There exist m e N, such that a_m = d."
>
> That is your uneducated or miseducated guess.
It is a theorem everywhere outside WM's wild weird world of
WMytheology.
Since d is constructed so that for all n, _n =/= a_nn,
It is also the case that for all n, d =/= a_n
> Prove it by finding any digit of d that is not, together will all its
> predecessors, in an a_m.
All the digits in d will be in some a_n at least as soon as that a_n
contains each of the digits from 0 up to (base - 1).So if the base is 10
and a_10 = 9876543210, then every digit in any d is in a_10.
But that only proves that WM as no idea about the true meanings of what
he is says.
> If there is a set of FISONs that contains every natural number n and all its
> predecessors, then this set cntains |N. Is there something in |N that is
> outside of all its FISONs?
Only in WM's wild weird world of WMytheology!
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