In article <firstname.lastname@example.org>, email@example.com wrote:
> On Tuesday, 18 June 2013 22:55:47 UTC+2, Zeit Geist wrote: > > > > Sorry, what was the point? > > > > > If you start counting from 1, you cannot have X numbers without a > > > number X in the ordinals. > > > I see you wrote: "No. Nothing works because w is the number of finite > > naturals, i.e., the number of digits of 0.111... There is no digit number > > w. But without a digit number X you cannot have X digits." > > > w is not a "digit number", and it need not be for it to be an Ordinal, or > > for its Cardinality to be aleph_0. > > Learn a bit modern set theory. There omega stands for ordinal and cardinal > number.
Not for those who choose to differentiate between ordinality and cardinality.
There are lots of different ordinals having cardinality aleph_0.
So the ordinality of omega + 1 and omega are different, but both are of cardinality aleph_0.
> > What Cantor used is false?
WM keeps claming it is, but most mathematicians disagree with WM, both on that issue and many, possibly most, other issues. --