So I've gone through the typical undergraduate math sequence (two semesters of real analysis, two semesters of abstract algebra, some measure theory, but I haven't taken discrete math) and in various posts online, I keep on seeing things such as $$O(x^2) $$ which I've never encountered in my formal education. What in the world does the big $O$ notation mean, to someone who's completely new to the notation, so that I understand how to use it? (It seems to me like a way to write "some polynomial stuff.")
I've also encountered "little" $o$ notation in studying for actuarial exams.
Also, why do we care about $O$ and $o$?