It is a kind of backwards reasoning that students empirically screw up all the time. Edit: so much so, that I would definitely recommend students rewrite these

It is a kind of backwards reasoning that students empirically screw up all the time. Edit: so much so, that I would definitely recommend students rewrite these proofs on assignments as an exerecise to make sure it's correct. By the time they reach a math PhD they probably don't need to do that anyomre. :)