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comment Prove that in a bit string, the string 01 occurs at most one more time than the string 10.
Sorry, not "equal number" but rather "no extra 01s".
Jan
5
comment Prove that in a bit string, the string 01 occurs at most one more time than the string 10.
If w ends in 0 then you must have an equal number of 01s and 10s. You can show this by looking at possibilities 1 and 2. This makes case 4 true, too. (Also, I don't think you deal with going from the empty string to a single-letter string. It is obvious, but your 4 cases assume w is non-empty.)