Continuity

• How to Make Any Function Repeat Periodically
  Turn a function on one interval into a periodic function using a modulo operation, with conditions for continuity and differentiability.
• When Is the Absolute Value of a Function Continuous?
  If f is continuous, then |f| is continuous. The converse is generally false, with a simple sign-changing counterexample.
• Does a Connected Graph Imply That a Function Is Continuous?
  A function can be discontinuous even when its graph is connected. The oscillating function sin(1/x), extended by f(0)=0, is a concrete example.
• Baby Rudin Chapter 4 Exercises 5 and 6: Solutions
  Solutions to Baby Rudin Chapter 4 Exercises 5 and 6: use the intermediate value theorem for constant sign and continuity to prove the zero set is closed.