Am Dienstag, 10. Dezember 2013 17:50:00 UTC+1 schrieb wpih...@gmail.com:
> > You have claimed many times that there is a list of all > > constructable real numbers.
No. Never. Since there is no "all numbers" of any infinite kind. I may have claimed: If there are all constructible numbers, then they form a countable set. A countable set is by definition a set that can be listed.
> You should consider what > > your admission that this list must be non-constructable > > means (Note you cannot have non-constructable lists without > > non-constructable numbers).
They would not help because only constructable numbers are under consideration.
But at present I assume the existence of a list of all rational numbers. (Also that is nonsense, but we assume it like assuming that there is a largest prime number in order to contradict it.) This list exist in matheology. And it leads to the contradiction that every rational number provably differs from the antidiagonal d but the antidiagonal provably does not differ from all rational numbers. Some matheologians want to make us believe that that is not a contradiction, but obviously it is.
Nevertheless I do not even attack this nonsensical claim but only state: There is no sequence of digits that allows to distinguish d from all rational numbers. That is all I claim.