Consider Cantor's diagonalization proof. Supply a rebuttal to the following complaint about the proof. "Every rationale number has a decimal expansion so we could apply this same argument to the set of rationale numbers between 0 and 1 is uncountable. However because we know that any subset of the rationale numbers must be countable, Cantor's diagonalization proof must be flawed."

Consider Cantor's diagonalization proof. Supply a rebuttal to the following complaint about the proof. "Every rationale number has a decimal expansion so we could apply this same argument to the set of rationale numbers between 0 and 1 is uncountable. However because we know that any subset of the rationale numbers must be countable, Cantor's diagonalization proof must be flawed."

Name: Consider Cantor's diagonalization proof. Supply a rebuttal to the fol
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Description: Consider Cantor's diagonalization proof. Supply a rebuttal to the following complaint about theproof."Every rationale number has a decimal expansion so we could apply this same argument to the setof rationale numbers between 0 and 1 is uncountable.

Advanced Engineering Mathematics

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Consider Cantor's diagonalization proof. Supply a rebuttal to the following complaint about the
proof.
"Every rationale number has a decimal expansion so we could apply this same argument to the set
of rationale numbers between 0 and 1 is uncountable. However because we know that any subset
of the rationale numbers must be countable, Cantor's diagonalization proof must be flawed."

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First, consider the following infinite collection of real numbers. Describe in your own words howthese numbers are constructed (that is, describe the procedure for generating this list of numbers). Then,using Cantor s diagonalization argument, find a number not on the list. Justify your answer.0.123456789101112131415161718 . . .0.2468101214161820222426283032 . . .0.369121518212427303336394245 . . .0.4812162024283236404448525660 . . .0.510152025303540455055606570 . .