Re: infinity


*** T. Winter wrote:
> In article <1127374594.506226.146060@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> albstorz@xxxxxx writes:
> ...
> > The infinite sequence {1},{1,2},{1,2,3}, ... has the maximum element
> > |N.
> > The infinite sequence of the cardinalities of the elements of this
> > sequence, namely |{1}|, |{1,2}|, |{1,2,3}|, ..., has the maximum
> > element "infinity".
>
> Both do not have a maximum element. I have no idea why you think they
> have one.
>
> > But the infinite sequence 1,2,3, ... has no maximum element.
> >
> > What is the difference between the first case of sequences and the
> > second case?
>
> None at all.
> --
> *** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
> home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/


It's really a funny world. If you put _infinitely_ many elements in,
step by step, you will never get infinity (Infinite steps, yes. But no
infinite set).
If you put in _infinitely_ many elements at once, you will have
infinity.

If you become aware of this difference you may understand why there are
no transfinite numbers.


Regards
AS

.