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

2. I forgot the particulars of another textbook that I read, not the one quoted below. It advises concluding $\delta -ϵ$ proofs with a littered, garnished $ϵ$ as in red below, because it's quicker to define a new ${ϵ}_2:=\text{ convoluted }{ϵ}_1$ 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.

posted almost 2 years ago

CC BY-SA 4.0

TextKit‭

64 reputation 11 2 0 26