Explain what the Continuum Hypothesis means and why this is important.

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 Cantors Theory*