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1. Show that the set of infinite sequences from is not countable.

Hint: Let be a function from to . Then is a sequence . Let . Then is again a sequence from , and for each we have . This method of proof is known as the Cantor diagonal process.

2. Show that is uncountable. (Use Problem 1)

Please see the attached file for the fully formatted problems.


Solution Summary

Countability is investigated. The solution is detailed and well presented.