Virgil
Posts:
7,025
Registered:
1/6/11


Re: Joel David Hamkins on definable real numbers in analysis
Posted:
Jun 28, 2013 3:09 PM


In article <83c237ac155b4ee28c6814d303d57722@googlegroups.com>, mueckenh@rz.fhaugsburg.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! 

