Week 1 - What, exactly, is a real number

Advanced Calculus came to a screaming halt today.

First, the students asked for some more information about sets and help developing intuition about upper bounds and least upper bounds.  We also discussed the difference between something being an element of a set and something being a subset and/or a proper subset.  Heads were nodding, so we continued on - for two questions.  What was the stumper?

• If x squared is 2, prove or disprove that x is a real number.

After a lot of head scratching, the class broke up and worked together on the boards for the rest of the time.

Everyone else was taking pictures of the board, so I decided to record a few myself.