Question: Problem 7. Define an (infinite) binary sequence s{0,1} to be prefix-repetitive if there are infinitely many strings w{0,1} such that wws. Prove: If the bits

Problem 7. Define an (infinite) binary sequence s{0,1} to be prefix-repetitive

Problem 7. Define an (infinite) binary sequence s{0,1} to be prefix-repetitive if there are infinitely many strings w{0,1} such that wws. Prove: If the bits of a sequence s{0,1} are chosen by independent tosses of a fair coin, then Prob[sisprefix-repetitive]=0. Note: xy means that x is a prefix of y where x is a string and y is a string or sequence

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