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I want to know if there is such book, with beautiful epsilon delta proofs of all kind.

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    $\begingroup$ I believe this and this may fit the bill. $\endgroup$ – Mark Fantini Aug 15 '14 at 2:01
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    $\begingroup$ It would be a very short book. $\endgroup$ – André Nicolas Aug 15 '14 at 2:35
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    $\begingroup$ In analytic number theory and elsewhere, there are wonderful theorems based on extremely delicate estimates. But I would not classify these as $\epsilon$-$\delta$ proofs in the usual sense. $\endgroup$ – André Nicolas Aug 15 '14 at 3:19
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    $\begingroup$ A great book is Calculus by Spivak. $\endgroup$ – NicNic8 Aug 15 '14 at 4:40
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    $\begingroup$ I'm giving this question a +1 just for the sheer audacity of asking for more epsilon-delta proofs after (I presume) sitting through some calculus courses $\endgroup$ – Yuriy S Apr 24 '18 at 7:49

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