|-|ercules says... > >Consider the list of increasing lengths of finite prefixes of pi > >3 >31 >314 >3141 >.... > >Everyone agrees that: >this list contains every digit of pi (1) > >as pi is an infinite digit sequence, this means > >this list contains every digit of an infinite digit sequence (2) > >similarly, as computable digit sequences contain increasing lengths of ALL >possible finite prefixes > >the list of computable reals contain every digit of ALL possible infinite >sequences (3) > >OK does everyone get (1) (2) and (3).
If you state it carefully, then yes, everyone gets it:
(A) Forall real numbers r, Forall natural numbers n, There exists a computable real r' such that r' agrees with r in the first n decimal places.
That fact has nothing to do with Cantor's proof. Cantor's theorem has the consequence:
(B) There exists a real number r, Forall computable reals r', there exists a natural number n such that r' and r disagree at the nth decimal place.
(B) is relevant to Cantor's theorem, but (A) is not.