The Mistakes Can Help

I've been reviewing mathematics and logic recently, because I'm planning on returning to university next year to study those subjects more. It may seem an odd step, but I personally find it odd that more philosophy students don't get drawn in by maths after they discover most of philosophy to be pretentious douchebags building theories and arguments from mist. But I probably feel this way because the way I was first introduced to philosophy was as a logic student in highschool, so it is perhaps more a return to a first love than anything else.

Anyway.

It strikes me that while answer sections in the back of the books are helpful, it can actually be beneficial for say, 2-3 percent of those answers to be mistakes. It not only keeps you thinking, it's also a reminder of the room for human error, and it also allows you the exhilaration of feeling that you got one up on the author of the textbook.

On a related note, Wolfram Alpha is a great way of settling the debate of whether your answer is right or the textbook's.