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Countable v. Uncountable: Prove that B* , the set of all finite strings over B = {0; 1} is countable, that is, B * can
Countable v. Uncountable:
Prove that B*, the set of all finite strings over B = {0; 1} is countable, that is, B* can be put in a one-to-one correspondence with the natural numbers N = {0, 1, 2,3,.....}. Hint: List the strings in B* in order of increasing length. Notice where the strings reset to all 0s.
strings |lambda 0 1 00 01 10 11 000 001 010 011 100 101 110 111 0000 0001
binary |0 0 1 0 1 2 3 0 1 2 3 4 5 6 7 0 1
n N |0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
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