Mathematics 242 – Principles of Analysis Definitions Quiz 5 – March 15, 2013

Your Name:

A) (5) Let f be a function defined on a deleted neighborhood of c. Define: lim_{x→c} f(x) = L.

B) (5) Let x_{n} be any sequence of real numbers. Must the sequence y_{n} = x_{n} − [x_{n}] have a convergent subsequence? Why or why not? (Note: As usual, [ ] denotes the greatest integer function.)