L03 · Sequences & Limits — Real Analysis-I

Convergence

$x_n\to x$ means: for every $\varepsilon\gt 0$ there exists $N$ such that $n\ge N\Rightarrow |x_n-x|\lt\varepsilon$ .

Visualization

Open interactive Section 3

Widgets: $\varepsilon$ - $N$ bands and extracting a convergent subsequence.