\magnification = \magstep1
\nopagenumbers
\leftline{Mathematics 242 -- Principles of Analysis}
\leftline{Definitions Quiz 5 -- March 15, 2013}
\medskip
\leftline{Your Name: $\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$}
\bigskip
\noindent
A) (5)  Let $f$ be a function defined on a deleted neighborhood of $c$.  Define:  $\lim_{x\to c} f(x) = L$.   
\vglue 4.0truein
\noindent
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.)   
\bye
