10.3, Due November 7

Difficult: Thanks to a friend, Jarred, I was able to follow and understand the proof that the interval (0,1) is uncountable.  However, if asked to reproduce this proof by memory, it would be difficult to do so with correct notation.  Indeed, it was also quite tricky when we proved that the sets (0,1) and the reals were numerically equivalent. How did they decide whether to use the plus or minus case of the quadratic formula? Their explanation was pretty vague. Are there any other functions that will be difficult to prove onto?

Also, maybe it would be helpful to show other examples where we try to construct a bijective function from two intervals . Like from the reals to (3,4), or from (-2,2) to reals, etc.

Interesting: The proof that the reals are uncountable was really slick!! I can see how that related to the homework assignment with the X’s and O’s. Also, it was interesting and helpful to draw a diagram with the concepts: finite, countable, infinite, uncountable, and denumerable.  It was helpful to see where these overlapped and how these concepts mapped together.