Hey, I'm adult but going to university for the first time, and I am taking Physics. My first semester is all about Math. Algebra and Analysis. I'm usually pretty good at math, but right now, we are "laying the foundation" for calculus, and of course all these things we took for granted over the years. This is proving to be an interesting challenge, which of course I suppose is good!. Anyways, my question is, what tips do you have to approach "proofs" or "show that", using certain axioms? Did you struggle with these at first? How long did it take you to begin to be able to show these? ex) let S be a nonempty subset of real numbers which is bounded below. Let -S denote the set of all real numbers -x, where x belongs to S. Prove that inf S exists and inf S = -sup(-S). So to show myself what was being asked, I just made an arbitrary set, S, and found the inf of my set and compared it to the -sup(-S) of -S. Of course it was equal. But how should I approach "prooving" it!.