Paper , Order, or Assignment Requirements

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*