Anyway, because I was such a ball of nerves I got a friend to quiz me with induction proofs that he’d yoinked off the internet so that I hadn’t seen them before. The proofs were of varying difficulty. One of them was the standard sum-type sort:
which is easy enough once you get the trick of splitting the summation into terms that can be induction-hypothesised (from base case to n) and extra terms (the n+1th term). Then it’s straightforward algebra to combine the two into something that looks like the induction hypothesis but with a quick change of variable n -> n+1.
The other was one that looked like:
which we saw later in I think the third week or so, and here you’re supposed to use the fact that the relation LessThan is transitive (so for A < B, and B < C, you know certainly that A < C) and a term-by-term comparison to show the B < C part. Then you’re essentially done.
Anyway, the rest is less a discussion about the proofs themselves and more about my ridiculous anxiety issues, which I really wish would just go away!