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Question: problem 8 define a 2coloring of 0 1 to be...

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Problem 8. Define a 2-coloring of {0, 1) to be a function X-(0, 1}* → {red, blue). (For example, i#x(1101)-red, we say that 1101 is red in the coloring c) of {0, 1) and every (infinite) binary sequence S E {0,1), there is Prove: For every 2-coloring a sequence o,,w2, of strings wn E 0,1 such that (i) S = u0wiw2 . . . , and (ii) wi, w2, w3,-.. are all the same color. (The string wo may or may not be this color.

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