I am currently enrolled in my first proof-based math course (Real Analysis), and so far I have absolutely loved it. It’s been incredibly difficult, but I’ve really enjoyed the challenge and the different type of thinking it requires.
However, one skill I’ve had a lot of trouble developing this semester is finding counterexamples when disproving something. I was wondering if anyone had any specific approaches or advice on how to go about finding these. I know that there’s not going to be some algorithmic approach that applies to every problem, but maybe just some things to consider or different ways of approaching it that could help a little?