From Randomness in Two Symbols to Randomness in Three Symbols

Abstract In 1909 Borel defined normality as a notion of randomness the digits representation real number over certain base (fractional expansion). If we think an infinite sequence symbols from finite alphabet A , can define directly for words : word x is normal to if every block appears with same asymptotic frequency in other length. Many examples have been found since its definition, being Champernowne 1933 first show explicit and simple instance. Moreover, it has characterized how select subsequences preserving normality, always leaving fixed. this work consider dual problem which consists inserting infinitely many positions given word, such way that preserved. Specifically, symbol b not present original solve insert resulting expanded ∪ { }.