User:IssaRice/Formalizing adjustment of epsilons: Difference between revisions
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==Tao's proof== | ==Tao's proof== | ||
In the first part of the proof, we suppose <math>x^2 < 2</math>, and let <math>0 < \varepsilon < 1</math>. Then we show the bound <math>(x+\varepsilon)^2 \leq x^2 + 5\varepsilon</math>. | |||
==The general case== | ==The general case== | ||
Revision as of 06:13, 24 May 2020
I want to elaborate on a thing that shows up when proving part (a) of https://taoanalysis.wordpress.com/2020/05/24/exercise-5-6-1/
Actually, a similar thing appears in Tao's original proof (Proposition 5.5.12) and the situation is simpler there (fewer variables to deal with), so let's start there.
Tao's proof
In the first part of the proof, we suppose , and let . Then we show the bound .