On Apr 7, 4:04 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 7 Apr., 10:54, fom <fomJ...@nyms.net> wrote: > > > > > > > > > > > When I failed to complete my education in > > mathematics, there had been little hope > > of any professional position. Whatever > > mathematical interests I might have chosen > > to pursue were not dictated on the basis > > of what would be beneficial to a > > professional status. > > > I had some tangential interest in the > > continuum hypothesis. I also believed > > that the resolution to the continuum > > hypothesis might be obtained by considering > > how the sign of equality is used. > > > It would be a mistake to think that I > > did not know what was involved with > > such a topic. > > Be sure, you did not know! > There is no finished infinity, no uncountability and therefore there > is no CH! > > Regards, WM
There is , at least such a thing as "relative unaccountability" . You can't enumerate the contents of an infinite integer list : 1 , 0 , 1 , 0 , 1 ......
There's always the "...." left out . However , you can unambiguously describe the infinite list by finite wording :
"an integer on the list has : Value 1 if it's on an 'even position on the list' . Value 0 if it's on an 'odd position on the list' .
This finite description unambiguously captures my 'infinite list' . Now , let's say I have a "countable list" of all integer sequences you could ever think off .
The point is, you can't think of a bijection between that list and N . This list appears uncountable to you , because it already contains every integer sequence you could ever think about . You'd run out of thoughts before you manage to construct an enumeration of my list .