Back to MA 375:

Summary 1:  Equivalence of sets

Even infinite sets can have different sizes. (.pdf)

Class Example 1:  Analysts Function

The following function exhibits wildly oscillating behavior.  Knowledge of it will forever change your intuition about real functions.

     

 

Class Example 2:  Modified analysis functions

 

 

Class Example 3Further modification

 

 

Class Example 4Another famous function

The graph?