# Continuity proof?

Let f be a continuous real valued function on $[0,\infty)$. Le t A be the set of real numbers 'a' that can be expressed as $a = \lim_{n\rightarrow \infty} x_n = \infty$. Prove that if A contains two numbers a & b, then it contains the entire interval with end points a & b.
Is there a typo here? How could a real number $a=\infty$?