How to find counterexamples in analysis proofs

[kostas230]

I'm not sure this is the correct section, but I have a problem. I'm a physics undergrad self-studying analysis from baby rudin, finishing Chaper 2. I seem to be able to work all the exercises and sometimes find other proofs to given theorems, but I have a problem in finding counter-examples in certain exercises. How should I study? What am I doing wrong? Thanks in advance :)

 

[UltrafastPED]

Many counterexamples are quite simple ... start from the proposed rule, and consider simple situations which might go wrong.

But even then you will find that ingenuity is required.