Am Donnerstag, 5. Dezember 2013 23:23:52 UTC+1 schrieb Zeit Geist:
> ~A: The Number x is Not a Ration Number. > > This is equivalent to saying: A( r e Q )( E( n e N )( x_n ~= r_n ) ).
Yes, an n in |N is required.
Santa Clause steps through the forest. His bag has a hole. With every step he loses 90% of the remaining contents. He goes and goes, very far, on and on. Is there any step where he has lost everything such that his sack is empty? Does the sequence 10^-n reach zero in any finite step? No.
But d must differ from every entry of the rationals-complete list in a finite digit. In mathematics we have no infinite step. And the number of steps is irrelevant.