October 17th (Week 6)

    Something that has been troubling me in MAT137 is the concept of the epsilon-delta definition of a limit. I find that the proofs in the textbook were lacking in a lot of explanation, and this lead to me staring at equations for hours trying to understand a proof. So, it is very helpful that CSC165 is also going over epsilon-delta proofs, as the formatting is much easier to understand in this course.
    I found that the thing that the MAT137 textbook was lacking for the proofs was explanations for what they were doing. While there is writing to explain a series of steps, having shorter comments for each step makes it much easier to understand. For example, in proving that the limit of x^2 as x goes to 3 is 9, a lot of the steps were very confusing.

    Where it says "At this point..." it explains what they are about to do. But why is x + 3 < 7? After a while I realized it is from 2 < x < 4 when 3 is added: 5 < x + 3 < 7. However, this is not immediately clear to the reader.This would be a better way to write that section of the proof:

|x - 3| < 1
Then 2 < x < 4
Then 5 < x + 3 < 7 (*)

|x + 3| ≤ |x| + |3|    #By triangle inequality
|x| + |3| = x + 3     #Since 2 < x < 4
By (*): x + 3 < 7
Then |x + 3| < 7
Then if |x - 3| < 1, |x^2 - 9| < 7|x - 3|