Answer
The golfer plays every hole on the course.
Work Step by Step
This problem provides the information necessary to conclude, using induction, that the golfer plays every hole on the course. The infinite number of holes on the course can be labeled one-to-one using the integers, and we have the base case that the golfer plays one hole. Finally, we know that if the golfer plays hole $n$, she plays hole $n+1$. Therefore, the golfer plays every hole on the course.
