I have presented the "distinguishability" argument. Which is an argument of intuition, it is not formalizable so far. The impression this argument imparts is that there are countably many reals?
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!
So which one we to believe?
The answer is Cantor's of course!
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.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.