Solution Found!
Let B be the set of all innite sequences over {0,1}. Show
Chapter , Problem 4.7(choose chapter or problem)
QUESTION:
Let B be the set of all innite sequences over {0,1}. Show that B is uncountable using a proof by diagonalization.
Questions & Answers
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 .