Question: Problem 7. Define an (infinite) binary sequence s {0,1) to be prefix-repetitive if there are infinitely many strings w E 0,1] such that ww s.

Problem 7. Define an (infinite) binary sequence s {0,1)" to be

Problem 7. Define an (infinite) binary sequence s {0,1)" to be prefix-repetitive if there are infinitely many strings w E 0,1] such that ww s. Prove: If the bits of a string s e [0,10 are chosen by independent tosses of a fair coin, thern Prob[s is prefix-repetitive] = 0. Note: y means that z is a prefix of y where z and y are strings

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