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I recently discovered the importance of examples and couter-examples in mathematics. Where could I find good examples books or anything related to it ?

I am particularly looking for rare limit-cases, but also representative examples (of a theorem, a concept, etc) in any mathematical subject including linear algebra and algebra.

Edit : I don't think this is a duplicate, because the link given has nothing about Algebra and linear algebra

I shall precise that I am looking for hard ones, not applied maths or classic 1st year illustrations.

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marked as duplicate by Najib Idrissi, vonbrand, Daniel Fischer, T. Bongers, abiessu Mar 4 at 21:52

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

    
    
You can also check out Favorite Counterexamples and Counterexamples in Algebra. –  Joe Johnson 126 Mar 4 at 20:40
    
@ Joe Johnson : thanks ! @ Amzoti : your link doesn't have algebra –  Julien__ Mar 4 at 23:46
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Two fantastic books that every mathematician should know are

Counterexamples in Analysis by Olmsted

Counterexamples in Topology by Steen and Seebach, already mentioned in the comments.

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Thanks, I already ordered them few days ago. I wish I knew same kind of books in algebra –  Julien__ Mar 4 at 20:43
    
[ can't vote up cause I am new to the site ] –  Julien__ Mar 4 at 23:32
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