
Re: Joel David Hamkins on definable real numbers in analysis
Posted:
Jun 28, 2013 5:02 PM


On Friday, June 28, 2013 1:34:49 AM UTC7, muec...@rz.fhaugsburg.de wrote: > On Thursday, June 27, 2013 11:54:40 PM UTC7, muec...@rz.fhaugsburg.de wrote: >
>> IF: An infinite collection of finite decimal sequences, when written in one line, makes an actually infinite collection, > >> THEN: an infinite collection of finite decimal sequences written in different lines does the same. > >> (Unioning over subsets cannot not extend a set.) > > There is no extension there, just consolidation.
Every F(n) is in some line. More cannot be consolidated.
> Just like U( { FISON } ) = U( { j  0 <= j <= n, n e N }) adds nothing new, it just puts them all in the single set N.
A union over subsets cannot put more than has already been there, because for every n, there has been FISON(n) in some line. Whether you call it consolidation or else: getting more than every FISON remains matheology without mathematical foundation.
> "Each child is on some bus" does not, necessarily, imply that "All children are on some bus".
Here we have a different situation: Each child is in one bus together with all smaller children. Try to figure out how many buses are required respectively possible.
Regards, WM

