The Course Towards a True Proof Never Did Run Smooth - Week 12

This week my focus has been mainly on the third and final assignment. As the course is coming to an end, I have been giving a lot of thought to all the different things I have learned. While overall, I feel like I have made a lot of progress, there are certain types of proofs that I continuously get caught up in. Any problem dealing with limits has proved to be quite a challenge. The first encounter with the epsilon delta proofs was quite overwhelming and while I made some progress in handling those type of proofs, I still feel that there is a lot more work that needs to be done. Furthermore, we have now been introduced to some calculus rules while dealing with limits. I do not have a lot of experience with calculus so now dealing with calculus in proofs feels like a very difficult challenge.

In general, developing an intuition about what a limit actually is can be quite difficult. I had a general idea, but it was still difficult to wrap my head around what a limit really is. I went to office hours this week to try and get a better grasp at what is going on.  Danny helped me out and gave me a written English sentence to try and understand what it means when a limit is approaching 0. He told me that the ratio you are using gets as close as we want to 0 provided we choose an “n” big enough.

Using the formal definition of a limit, we get:

"c e Â⁺, $n_c e À, "n e À, n ³ n_c Þ (ratio that has a limit that approaches 0) < c.

This fits the loose definition that Danny gave me and brings more understanding to the more formal way of putting it.

This assignment has allowed me to practice these types of questions and forced me to try and gain a better understanding of what a limit is. I don’t think by the end of the course, I will have a full grasp but I will definitely know a lot more than when I first came in. That in itself makes it worth the effort.