Right. IMHO that's one of the few valid reasons to require some basic understanding of mathematical rigor in programming. The mindset that you need to deal with

Right. IMHO that's one of the few valid reasons to require some basic understanding of mathematical rigor in programming. The mindset that you need to deal with ALL, 100%, of the cases instead of just settling for "90% is prolly enough" is very important to counterbalance these common tendencies you speak of.