Hoping to make like an alternating series that converges...

CSC165 for me, seemed to contain a lot of flailing about and stabbing in the dark.

I feel less like I am randomly messing around with numbers and logic symbols, and more like I have an organized attack, and I find I am actually enjoying the material now.
Which honestly, is something I never thought I would think.
I was... prepared to hide in a fortress and battle the course down when I began this semester.

But, I started on a totally different mindset this time around (I think I gave up before I even tried in CSC165), and I enjoyed doing the assignment 1, well mostly, I still have part 3b left.

I wrote out proofs for questions 1 and 2 from A1 on Wednesday as the actual intuitive reasoning behind them wasn't that hard to see, and went to the TA hours on Thursday morning, to make sure someone besides me could understand it, and that I was indeed actually proving something.
(And with some advice to clear some fog in my writing, it seemed that I was.)

I also didn't understand what I actually had to prove for 3a, so I went to ask about that as well, but another student asked about it before me, so it's nice to know I was not the only one who couldn't figure out the question.
I wrote the proof up yesterday morning, and I have some confidence in it...

Yesterday, after seeing the second invalid proof in the lecture, I started to get really scared that I would write proofs like that. I think I may be forever haunted by the hexagon proof. The seemingly glaringly obvious truth that hides lies?
AH!!

--------------------

And something that has been bugging me is using n = 0 as a base case.
Because the conventions used like n^0 = 1 and 0! = 1 can sometimes make a base case valid when it shouldn't be, or invalid when the statement works for other numbers. And sometimes it seems that n^0 = 0 makes more sense.

And also, the fact that the set of all real numbers can be defined as open or closed, with the empty set then defined as the opposite, makes me confused as well.
Why this flexibility here?
In my MAT237 lecture, we were given a counter example to a statement that included the fact that the reals was a open set. But if the reals can be defined as open or closed, is that really a good enough counter example?
My first reaction was that it was very weak and I was rather disappointed with the example since it didn't lead to a very concrete reason why the statement failed, but instead left me more confused.