"Peter Webb" <webbfamily@DIESPAMDIEoptusnet.com.au> wrote > "|-|ercules" <email@example.com> wrote in message > news:87ocucFrn3U1@mid.individual.net... >> 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) >> > > Sloppy terminology, but I agree with what I think you are trying to say. > >> as pi is an infinite digit sequence, this means >> >> this list contains every digit of an infinite digit sequence (2) >> > > Again sloppy, but basically true. > >> similarly, as computable digit sequences contain increasing lengths of ALL >> possible finite prefixes >> > > Not "similarly", but if you are claiming that all Reals which have finite > decimal expansions can be listed, this is correct.
You didn't follow the similarity.
Given the increasing finite prefixes of pi
3 31 314 ..
This list contains every digit of the infinite expansion of pi.
Given the increasing finite prefixes of e
2 21 218 ..
This list contains every digit of the infinite expansion of e.
Given the increasing finite prefixes of ALL infinite expansions, that list contains every digit of every infinite expansion.
So (3) is true.
> the list of computable reals contain every digit of ALL possible infinite > sequences (3)