How does an indirect proof work?

"Indirect proof, also known as a proof by contradiction or reductio ad absurdum, starts in a completely opposite way. It says, “okay, I’m trying to prove X. Well, suppose for the sake of argument I assume that the opposite—not X—is true. Where would that lead me?” If you follow all the rules and it leads you to a contradiction, this tells you that the original assumption of ¬X must have been false. And this in turn proves that X must be true. We do this all the time in our thinking. Say you’re driving down the highway. How do you know that the alternator in your car engine is working? A direct proof would require that you open the hood and examine the part, testing to ensure it works properly. An indirect proof simply says, “well, suppose it weren’t working properly. Then, my car engine wouldn’t operate. But here I am, driving down the road, and the engine obviously does operate, so that tells me that the alternator must be working properly.”"