> with an infinite number of decimals. Now it is true that there > are algorithms that output certain numbers with an infinite > number of decimals. For example, one such algorithm is to always > output 3, another is to encode one of the ways of computing the > digits of pi, and still another is to concatenate (in the appropriate > order) the algorithms you alluded to in order to output the > number 0.1234567891011121314...9899100101102103... Note that > this last number has every finite decimal string appearing > (infinitely many times, in fact), so we don't have to appeal
By the way, when I said "to concatenate", you can't always concatenate algorithms to get an algorithm. However, in this case each of the algorithms has a "finite run time", so I think we're O-K by doing this here.