On 8 Dez., 19:36, A <anonymous.rubbert...@yahoo.com> wrote:
> > A function f is said to be continuous at a point x in its domain if > the limit of f(a), as a approaches x, is equal to f(x); in others > words, the limit of the values of f is equal to the value of f at the > limit, speaking loosely. Of course, not every function is continuous > at every point in its domain, and some functions are not even > continuous at any point in their domains at all. > > The situation for sets and cardinality is no more mysterious than > that. The cardinality of a limit of subsets of the integers is not > guaranteed to be the limit of the cardinalities of those subsets. You > don't expect an arbitrary function to always be continuous, so perhaps > it's unreasonable to expect the cardinality "function," defined on > subsets of the integers, to be continuous.-
That depends on the circumstances. If infinite sets exist, then they have a cardinality. Then the limit cardinality is the cardinality of the limit set.
If they do not exist but are merely an arbitrary, perhaps inconsistent delusion, then everything is possible. I argue, based on Cantor's claim, that infinite sets exist (in order to show that they do not).