I tore the cartilage in my knee, and the pain is severe. I've heard that cartilage doesn't have any nerves, so why does my knee hurt so much?

You're right that nerves signaling pain don't connect to articular cartilage. So why the pain? Swelling in or around the joint could be one explanation. This can put pressure on the nerves within the knee joint that do signal pain. If the articular cartilage is torn completely through to the bone below it, then the pressure over the unprotected part of the bone could be registering pain because these tissues in the bone have a nerve supply.