Contemplating the Infinite

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If you’ve never thought much about the idea of “infinity” before, then the Great Theorems of Chapters 11 and 12 might be a little surprising. If you’ve seen them before, it’s always good to stop and think a bit about why these theorems are surprising. The historical context in the readings in Dunham should help.

For fun, you might try to explain to a (non-mathematician) friend that there are infinite sets which are the same “size”, and infinite sets which are different “sizes”. You’ll first have to explain what you mean by “size”, of course! The second reading might help your explanation, since it can be used effectively in a high school classroom for talking about this topic.

Readings

First reading: Dunham, Chapters 11 and 12

Second reading: The Infinite Hotel.

If you prefer watching instead of reading, here’s a video on the same topic as the second reading. How an Infinite Hotel Ran Out of Room

Questions

After the hotel appears to be full, a family arrives and asks for a room. After moving the patrons around, which room is the new family assigned? $\answer [given]{1}$

In the story of “Hotel Infinity”, what does George build, other than the hotel?

A fleet of buses. A courtroom. Billboards. An infinite parking garage.