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Which other Real Analysis textbooks unusually recommend ending delta-epsilon proofs with a cluttered, bedecked $\epsilon$? [closed]

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Closed as too generic by Mithical‭ on May 17, 2023 at 03:48

This post contains multiple questions or has many possible indistinguishable correct answers or requires extraordinary long answers.

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  1. Most textbooks conclude $\delta-\epsilon$ proofs tidily with $\epsilon > 0$ alone, as in red beneath. But what's the official term for this alternative $\delta-\epsilon$ proof, as in green beneath?

  2. I forgot the particulars of another textbook that I read, not the one quoted below. It advises concluding $\delta-\epsilon$ proofs with a littered, garnished $\epsilon$ as in red below, because it's quicker to define a new $\epsilon_2 := \text{ convoluted } \epsilon_1$ at the end (rather than working backwards to deduce byzantine, unkempt $\delta$'s). Please recommend such textbooks?

Image alt text

Frank Morgan, Real Analysis (2005), pages 17-8.

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x-post https://math.stackexchange.com/questions/4700888/which-other-real-analysis-textbooks-unusually... (1 comment)

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