This is also useful to understand preconditions by reduction. I.e. if you want to understand a theorem, it can sometimes be useful to start by figuring out the reason behind the preconditions. "Why does this apply only to balls that have hair?" Simply go, "What would the theorem imply if I start with a smooth ball instead?"
This practise can also lead to generalisations. Oftentimes starting with a smooth ball will make you go "What? That't can't be possible."
But sometimes, starting with a smooth ball leads you to, "Huh, that's really, really weird. But it's not a contradiction in and of itself. I could use that result in another context!"
This is also useful to understand preconditions by reduction. I.e. if you want to understand a theorem, it can sometimes be useful to start by figuring out the reason behind the preconditions. "Why does this apply only to balls that have hair?" Simply go, "What would the theorem imply if I start with a smooth ball instead?"
This practise can also lead to generalisations. Oftentimes starting with a smooth ball will make you go "What? That't can't be possible."
But sometimes, starting with a smooth ball leads you to, "Huh, that's really, really weird. But it's not a contradiction in and of itself. I could use that result in another context!"