Week 6: More on proofs.

So the week after Thanksgiving we learned more about how to write proofs. For example given a definition and something you have to prove, assume/define and pick as much as you can before you start writing the proof. Mostly to help with the format and leading our proof to where we want to go. I prefer the way that we're learning about proofs in this course more than MAT137 where we're only really given an example of a proof and we're just expected to reproduce that format without much explanation on each individual part of it. So we learned about Proof by cases and Epsilon Delta proofs (Which I don't think are called that in the slides when we learned about it but it was essentially this.)

So as I previously mentioned the way that we learn to write proofs in this course is different and much more structured (Which I think is much more helpful to students learning about this for the first time). So for the proof of a limit that was shown in class, the proof was done more differently than how I learned it; Rough work wasn't separated and for example:

For all ϵ...0 < |x-3| <𝛿 => |x²-3²| < ϵ

It was written as 𝛿|x-3+3+3| instead to manipulate |x+3| into |x-3|. I found this method in a way more straightforward than making |x-3| < 1 and making intervals but I feel like the way we learned it here won't work for functions where there might be say, square root symbols. Now I've only briefly thought about this fact and have not tried a more complicated limit proof with this method so I could be wrong. But overall I did find the way we learned it in this course more intuitive in a sense so that's pretty good!