Explore BrainMass
Share

Countability

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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.

© BrainMass Inc. brainmass.com March 21, 2019, 3:09 pm ad1c9bdddf
https://brainmass.com/math/real-analysis/real-analysis-countability-143101

Attachments

Solution Summary

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

$2.19