Comments on Which other Real Analysis textbooks unusually recommend ending delta-epsilon proofs with a cluttered, bedecked $\epsilon$?
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Which other Real Analysis textbooks unusually recommend ending delta-epsilon proofs with a cluttered, bedecked $\epsilon$? [closed]
Closed as too generic by Mithical on May 17, 2023 at 03:48
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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?
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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?
Frank Morgan, Real Analysis (2005), pages 17-8.
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