Let B be the set of all innite sequences over {0,1}. Show

Chapter , Problem 4.7

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QUESTION:

Let B be the set of all innite sequences over {0,1}. Show that B is uncountable using a proof by diagonalization.

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QUESTION:

Let B be the set of all innite sequences over {0,1}. Show that B is uncountable using a proof by diagonalization.

ANSWER:

Step 1 of 2

Given that, each element in is infinite. Consider the sequence of bits as:  where each bit is a 0 or 1.

Assume that is countable, then there exists a correspondence  between and . For an integer , consider the function as :

, where  is the  bit of sequence .

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