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Re: Joel David Hamkins on definable real numbers in analysis
Posted:
Jun 28, 2013 5:25 PM
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On Friday, June 28, 2013 2:02:23 PM UTC-7, muec...@rz.fh-augsburg.de wrote:
> On Friday, June 28, 2013 1:34:49 AM UTC-7, muec...@rz.fh-augsburg.de wrote:
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> > On Thursday, June 27, 2013 11:54:40 PM UTC-7, muec...@rz.fh-augsburg.de wrote:
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> >> IF: An infinite collection of finite decimal sequences, when written in one line, makes an actually infinite collection,
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> >> THEN: an infinite collection of finite decimal sequences written in different lines does the same.
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> >> (Unioning over subsets cannot not extend a set.)
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> > There is no extension there, just consolidation.
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> Every F(n) is in some line. More cannot be consolidated.
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> > 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.
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> 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.
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I feel great pity for you, if you can't comprehend a strictly increasing unbounded
sequence.
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> > "Each child is on some bus" does not, necessarily, imply that "All children are on some bus".
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> 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.
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That just shows how much of a child you are.
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> Regards, WM
ZG
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