In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 17 Jan., 08:42, Ralf Bader <ba...@nefkom.net> wrote: > > > In a similar way it seems to be > > impossible for Mückenheim to grasp something actually (not in the > > always-growing sense) countably infinite without a boundary at the far end. > > Not at all! I consider and vivdly imagine the actually infinite set of > all terminating decimal representations of the reals containg all > natural numbers as indices. Alas I cannot imagine that there is > another decimal representations of the reals which deviates from all > of them. Can you? > > Regards, WM
Easily! Any negative real number, as there will also have a sign. And any real of absolute valueof 1 or greater as these numbers will have digits indexed with non-natural integers.
And then there are all those uncountably many that no one can imagine specifically but must exist if the ral number fiels is to satisfy its own requirements.. --