Jost - Postmodern analysis
Chapter 0 - Prerequisites
Problem 0.1 : Show that $a \in \mathbb{R}$ is an accumulation point of a sequence $(a_n)_{n \in \mathbb{N}} \subset \mathbb{R}$ precisely if for all $\varepsilon > 0$ and all $N \in N$ there exists $n \geq N$ with \begin{equation} |a_n - a| < \varepsilon \end{equation}
Solution :