I was reading a book on coding theory, there was a definition fot the Hamming's Distance and also one example. Understanding purely from the definition was hard but the example helped to give meaning to the definition. I felt the same when reading some other books so as I'm still self-learning mathematics, I just got this curiosity:
Is it a problem to understand mathematical definitions only with examples? Should I aim at a level of understanding with definitions only? Will this level eventually come?
It may be a naive question, but I feel insecure of bulding wrong study practice. I'm a also a piano student, when reading about piano study I've discovered that it's study isn't really intuitive then I've expanded and started to get worried also with studying habits for other things I study.