He (whoever he is) might have meant that infinity is not a real number. In that, he's correct. However, to write a limit as the one given as +infinity or -infinity is valid. I quote from wikipedia:
Limit (mathematics) - Wikipedia, the free encyclopediaA related concept to limits as x approaches some finite number is the limit as x approaches positive or negative infinity. This does not literally mean that the difference between x and infinity becomes small, since infinity is not a real number; rather, it means that x either grows without bound positively (positive infinity) or grows without bound negatively (negative infinity).