Normal or not normal? If a work can be found in pi, then one would think a Finite State Gambler (FSG) would succeed on the portion of pi equivalent to the work. But FSGs cannot succeed on normal sequences, meaning this sequence would be non-normal.
Of course this begs the question of whether a number normal over an infinite sequence can contain sub-sequences that are non-normal - sequences of 100 tails will occur in sufficiently large completely normal (randomized) sequences of random coin tosses, e.g.
Comments
Normal or not normal? If a work can be found in pi, then one would think a Finite State Gambler (FSG) would succeed on the portion of pi equivalent to the work. But FSGs cannot succeed on normal sequences, meaning this sequence would be non-normal.
Of course this begs the question of whether a number normal over an infinite sequence can contain sub-sequences that are non-normal - sequences of 100 tails will occur in sufficiently large completely normal (randomized) sequences of random coin tosses, e.g.
A normal sequence includes all non-normal sequences, by definition of normality.