Respond to these questions below: – Describe how you would approach a proof that two infinite sets have the same cardinality. Examples you might consider include |Z| = |2Z|, |N| = |N0|, or |(0,1)|=|R|. – Explain the main ideas behind the argument that Q is a countably infinite set. What does it mean for a set to be countable? – Explain the main ideas behind the argument that (0,1) [and hence R] is uncountably infinite. What does it mean for a set to be uncountable? – What does it mean for one ?size of infinity? to be ?larger? than another? – How would you explain these ideas to a person who has not studied mathematics at this level? – Explain what the Continuum Hypothesis means and why this is important. – Discuss the historical context and/or the philosophical implications of Cantor’s Theory*
