In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> 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.
A decimal, or other base, expression is not a actually a number but merely a numeral, a representation of or name for a number.
Actually, no real can be distinguished from ALL others by ANY finite initial segment of its decimal, or other base, representation. > > > > 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
Only in WMytheology is ANY real distinguishable from all others by ANY finite initial segment of its decimal, or other base, representation.
> because > no infinite diagonal of a Cantor list can be defined other than by its > finite initial segments (or a finite definition).
A finite definition can determine infinitely many digits in a real number's decimal, or other base, representatoin.
> because Cantor by distinguishing real nunbers "proved" the existence > of indistinguishable "real" numbers. (He would rotate in his grave > after reading this.)
After reading WM's misrepresentation of is ideas, quite likely. > > > 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.
With WM being a primary example of brain blockage! --