|-|ercules says... > >"Peter Webb" <webbfamily@DIESPAMDIEoptusnet.com.au> wrote >> "|-|ercules" <radgray123@yahoo.com> wrote in message >> news:87om34FahrU1@mid.individual.net... >>> "Peter Webb" <webbfamily@DIESPAMDIEoptusnet.com.au> wrote >>>> "|-|ercules" <radgray123@yahoo.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. >>> >> >> But pi doesn't appear on the list. >> >> So? > > >that doesn't matter, because that's a convergent sequence.
That's *all* that matters, for Cantor's theorem. The claim is that for every list of reals, there is another real that does not appear on the list.
