Am Montag, 10. Februar 2014 09:38:24 UTC+1 schrieb thenewc...@gmail.com: > On Monday, February 10, 2014 10:08:58 AM UTC+2, Virgil wrote:
> > The real numbers are not countable because they don't exist.
That depends on the definition. I accept pi or sqrt(17) as real numbers although I know that these numbers cannot be represented but only approximated by strings of digits.
> Here is a proof that D.Cuts do not define irrational numbers:
In my opinion the expression LIM(1 + 1/n)^n defines e. I accept that (although it is impossible to find all digits) because we can calculate the string of digits up to every desired precision eps > 0. >
> > Now, if you assume that all "real" numbers can be represented as decimals, then I have proved (irrefutably), that the real numbers are indeed countable,
That is certainly correct because the premise is false.