How to read mathematical definitions, theorems, etc. I'm hoping someone can give me some advice on how to read and extrapolate information from Mathematical definitions, theorems, etc. 
I understand that I need to read it till I understand what it means and to find examples to fit it. But it's not really doing anything for me. I'm spending more than 30 minutes on each definition/theorem but I don't know what the quickest method is for understanding these things. 
here's one theorem that doesn't make sense to me
Theorem 2.4 (Cantor) No interval (a,b) of real numbers can be the range of some sequence
I'm currently reading Elementary Real Analysis and Abstract Algebra books and some of the definitions are pretty gnarly. 
 A: When it comes to definitions, I'd follow the advice of Hilbert: 

One must always begin with the simplest examples.


Math gets easier the more concrete it feels. Give yourself something simple to chew on before considering more complicated examples. If you're learning about, say vector spaces, spend some time just thinking about $\mathbb{R}^2$ for a night. I find that I understand most complicated examples by "projecting" them onto a simpler example where my intuition is stronger and then applying my result to the more complicated case. 
There is no general formula for understanding theorems, or definitions for that matter. Besides reading slowly and making sure you understand the smallest details, I'd offer one further piece of advice, which I believe I read on MSE at some point. Once you understand the theorem, try to imagine how the theorem could  not be true. Then, you'll find yourself mildly astonished by the time you hit the QED. I've always found this helps theorems "stick" with me more. 
