But think about what a limit is. Think of X and Y as their own functions. so something more like X(g) / Y(g). As g increases, X and Y can take any path across the plane that they want. We get to arbitrarily choose what X and Y are. All we are doing is describe how our limit behaves as we slide along the scale towards infinity. Just because g increased by went from 10 to 11 doesn't mean that X and Y behaved the same way. We can arbitrarily choose X and Y such the limit as g approaches infinity is 0 for both, but the way that X and Y are changing is different. Like the example above, if we choose X and Y such that X(g)/Y(g) is 17 for all g, but the X and Y both approach 0 as g approaches infinuty, then as g approaches infinity X and Y go to 0, but X / Y (0 / 0), goes to 17. It's not a true 0/0, because the functions we chose got to 0 at different rates.
