On 20 Jun., 02:04, "Mike Terry" > > No, you're misunderstanding the meaning of computable. > > Hopefully you will be OK with the following definition: > > A real number r is computable if there is a TM (Turing machine) > T which given n as input, will produce as output > the n'th digit of r.
Whatever might be the true meaning: The Turing machine need a finite definition. Therefore the computable number has a finite definition.
There are only countable many finite definitions. And every diagonal of a defined Cantor list has also a finite definition.
Therefore Cantor shows that the countable set of all real numbers with finite definitions is uncountable (or that the defined diagonal number is undefined).