On 2 Jan., 22:19, Zuhair <zaljo...@gmail.com> wrote:
> On the other hand Cantor have presented many arguments all of which > are rigorously formalized in second order logic under full semantics, > and those arguments PROVED that there are uncountably many reals
that can be distinguished by their finite initial segments. > > So which one we to believe? > > The answer is Cantor's of course!
So let us believe that uncountably many real numbers can be distinguished by their countably many finite initial segments, because no infinite diagonal of a Cantor list can be defined other than by its finite initial segments (or a finite definition). > > Why?
because Cantor by distinguishing real nunbers "proved" the existence of indistinguishable "real" numbers. (He would rotate in his grave after reading this.)
> Because Cantor's arguments are very clear, and are formalizable in an > exact manner, so they are quite understandable and obvious. While the > distinguishability argument of mine is actually ambiguous and shredded > in mystery.
No, every sensible formalization requires finite distinguishability.
> The Consideration step in that argument and the analogy of > that with the Generalization step in that argument is really just an > intuitive leap nothing more nothing less. > > This only demonstrates how common intuition fail at absolute infinity.
This demonstrates that Cantor's argument has created thousands of matheologians who have a block in their brains.