Limit existence and infinity

One if the awesome things about studying on my own, is the flexibility of choosing my own schedule and resources. The drawback, as I have mentioned before, is that different resources have different points, methods and even explanations. If your resources also vary in timeframe, those issues become more apparent. Let's take for example the limits of 1/x as x approaches 0 from the negative and from the positive side.

If we look at a graph of 1/x we can see that as x approaches 0 from the negative side, the graph starts to approach the y axis but not touch it. Since x cannot be 0 (1/0 is undefined), then the y axis, where x=0, is an asymptote, a line that will never be touched by the graph. That means that our graph will get closer and closer to the y axis for all infinity without touching it. Therefore the limit of 1/x as x approaches 0 from the negative side, in the strictest definition of a limit, does not exist and that is how my text book defines it.

My online class however, also defines this limit as negative infinity and as positive infinity when you approach 0 from the positive side. The Profesor explained that it was a more informative way to describe the limit of 1/x as x approaches 0.

My problem came along when I did my textbook homework after my online lesson. While I was checking my answers I noticed I had gotten two incorrect ones. They were the limits described above. In the textbook the right answer was that the limits did not exist, I had answered that they were positive and negative Infiniti. Being a student on my own, I had to retrace my steps, watched my class again and do a lot of research to find out if I had gotten the right answer. When I reviewed my online lesson I heard the explanation the professor made about these limits not existing and how using infinity gave us more info about what was happening.

If I had not been able to re-watch my class, I would probably still be looking for the answer. In a traditional classroom my doubt would have been put to rest in a second by the teacher. On my own I had to figure it out myself. I see advantages and disadvantages to both situations.

How about you?