Finding Counterexamples in Analysis: Tips and Tricks

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The discussion focuses on the challenges of finding counterexamples in mathematical analysis, particularly for a physics undergraduate studying from "Baby Rudin." Participants suggest starting with the proposed rule and examining simple cases where it might fail. They emphasize that while some counterexamples are straightforward, creativity and ingenuity are often necessary to identify them. The importance of practice and familiarity with concepts is highlighted as essential for improving this skill. Overall, developing a systematic approach to analyzing rules can enhance the ability to find counterexamples effectively.
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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 :)
 
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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.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

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