Virgil
Posts:
8,833
Registered:
1/6/11


Re: Joel David Hamkins on definable real numbers in analysis
Posted:
Jun 29, 2013 3:36 PM


In article <dc2a184e166c4af7afc25c752a95469b@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Friday, 28 June 2013 23:25:22 UTC+2, Zeit Geist wrote: > > > > > > I feel great pity for you, if you can't comprehend a strictly increasing > > unbounded sequence. > > O, I can. I cannot, however, comprehend that it has a limit.
What is unbounded in one space may well be unbounded in a larger space. The ordered set of reals is unbounded but its twopoint compactification IS bounded, so that increasing sequences with no limit in the former have a limit in the latter.
Or spelled out > frankly, I can prove that it hasn't a limit, if mathematics is valid, i.e., > if the limit of the sequence > a_n = min(100, (N  F(n))) > has to be calculated as our master Cauchy has taught us. Since it is a constant sequence, its limit by any standard is its constant value of 100. At least until WM can find an n in N foe which (N  FISON(n)) < 100 

