This article was designed to explain what exactly an epsilon-delta proof is and to demonstrate an example of such a proof. Although these proofs are of lit- tle practical use, they still offer key insight into what a limit actually is. In addition, they often require mathematical creativit...
Explore the epsilon-delta definition of limit. Find delta given epsilon, and discover how to evaluate limits using the epsilon-delta proof method...
Learn the definition of Epsilon delta proof and browse a collection of 28 enlightening community discussions around the topic.
THE EPSILON-DELTA DEFINITION OF A LIMIT In the beginning … In the beginning … Leibniz and Newton created/discovered Calculus Calculus soon became the mathematics of change. Calculus studied rates of change (derivatives) and accumulated change (integrals). ...
Answer to: Give an epsilon-delta proof of the limit fact. Limit as x approaches 0 of (4x + 6) = 6. By signing up, you'll get thousands of...
理解这里的赋值是本次证明的难点和精髓所在,很显然这个取值是构造出来的,它既要满足\delta\lambda N的取值范围,又与N、\lambda这些假设中的常量有关,在后面的推导中可以与chernoff不等式的bound联动,从而产生奇妙的反应。对于该取值,Roman先生的解释是,他想让不等式右面小于\frac{1}{num \space of\space net-int...
Answer to: Use algebra, but not an epsilon delta proof to find \lim\limits_{x \rightarrow a}\frac{x^4 - a^4}{x - a} By signing up, you'll get...
The first two judges I had were mathematics judges. The first one asked me what I would do if I were giving a talk about my project at a colloquium. He asked me to explain one of my results, which I initially did incorrectly (having not looked through the older proof in quite some ...
The first author recently proved\nthat any graph satisfying $\\omega > \\frac 23(\\Delta+1)$ contains a stable set\nintersecting every maximum clique. In this note we exploit the latter result to\ngive a much shorter, simpler proof of the former. We include, as a certificate\nof ...
-john domain. we will postpone the proof to sect. 3.2 , which may be of independent interest. this is the main reason why we have introduced these domains; if we can establish estimates in domains \(\omega _r(x_0)\) where the associated constant only depends on \(\delta ,\) ...