|N, we use Cantor's Diagonal Method, where we change the nthdigit dnn of the nth number rn E (0, 1) in a purported fixed list of all numbers r e (0, 1)by changing dnn to dm1 if dnn + 1 and letting...

Extracted text: 10. In the proof that |(0, 1)| > |N, we use Cantor's Diagonal Method, where we change the nth digit dnn of the nth number rn E (0, 1) in a purported fixed list of all numbers r e (0, 1) by changing dnn to dm 1 if dnn + 1 and letting dnn 2 otherwise. Then we form a number r* 0.d d, ... and claim that because r* is not in the purported list, therefore |(0, 1)| > |N|. State the function used in the proof clearly and, using the definition of two sets being equal in cardinality |A| = |B|, explain why the proof shows that the cardinality of (0, 1) is strictly bigger than the cardinality of N.