My question is related with the definition of Cauchy sequence As we know that a sequence $(x_n)$ of real numbers is called Cauchy, if for every positive real number ε, there is a positive …

Jun 8, 2016 · I have a question regarding the definition of a Cauchy sequence of a sequence in a metric space. The definition I learned and that is consistent with Wikipedia defines a sequence …

Apr 30, 2017 · For instance, in $\mathbb Q$ with the standard metric, any sequence of rational numbers that converges in $\mathbb R$ to an irrational number is Cauchy but fails to …

Aug 25, 2023 · Both these theorems were discussed in class, I wanted to discuss some doubts regarding theorem 1. Is it possible to say simply from theorem 1 alone that any sequence for …

Dec 27, 2015 · I have shown an example of how to use the definition of a Cauchy sequence. I changed the sequence to an easier one (to be honest because the one you suggested looked …

Jul 2, 2020 · How to prove that a sequence is Cauchy Ask Question Asked 5 years, 5 months ago Modified 5 years, 5 months ago

1 In informal terms, a sequence $\sigma=\langle x_n:n\in\Bbb N\rangle$ is Cauchy if no matter how small a positive $\epsilon$ you take, you can find a tail of the sequence whose terms are …

Jan 29, 2023 · 4 Context: The real numbers were constructed using Cauchy sequences of rational numbers, where every real corresponds to the equivalence class of a rational Cauchy …

Nov 25, 2017 · Show directly that $x_n = {n+1 \over n}$ is a Cauchy sequence Ask Question Asked 10 years ago Modified 8 years ago

Prove that sequence {(2n+1)/n} is Cauchy. I understand the definition of a Cauchy sequence; however, I'm not sure how to find the necessary value of N to satisfy the prove. I know that …