On 8 Dez., 15:22, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> > I said you can take it from the shelf. It is not defined as a limit > > (if you like so) although amazingly omega is called a limit ordinal.
> Yes, it is called a limit ordinal because by definition each ordinal that > has no predecessor is called a limit ordinal (that is the definition of the > term "limit ordinal"). It has in itself nothing to do with limits.
No, that is not the reason. The reason is that omega is a limit without axiom of infinity, and omega is older than that axiom.
> > N is a concept of mathematics. That's enough. > > Yes, and it is a concept of mathematics because it is defined within > mathematics, and it is not defined as a limit.
It is a concept of mathematics without any being defined.
> > The infinite union is a limit. > > I do not think you have looked at the definition of an infinite union, if > you had done so you would find that (in your words) such a union is found > on the shelf and does not involve limits. Try to start doing mathematics > and rid yourself of the idea that an infinite union is a limit.
An infinite union *is* not at all. But if it were, it was a limit. > > > Why did you argue that limits of > > cardinality and sets are different, if there are no limits at all? > > I have explicitly defined the limit of a sequence of sets. With that > definition (and the common definition of limits of sequences of natural > numbers) I found that the cardinality of the limit is not necessarily > equal to the limit of the cardinalities.