Example: air traffic controller
Search results with tag "Cauchy sequence"
Complete Metric Spaces - Chula
pioneer.netserv.chula.ac.thComplete Metric Spaces Definition 1. Let (X,d) be a metric space. A sequence (x n) in X is called a Cauchy sequence if for any ε > 0, there is an n ε ∈ N such that d(x m,x n) < ε for any m ≥ n
Compactness in metric spaces - UCL
www.ucl.ac.uk1 2m−1 1 2m 1 2n−2 (2.2b) ≤ 1 2m−2, (2.2c) which shows that (xn) is a Cauchy sequence in X.Since X is complete, the sequence (xn) converges to some point a ∈ X. Now let α0 ∈ I be an index such that a ∈ Uα0 (why must such an index exist?). There exists ǫ > 0 such that B(a,ǫ) ⊆ Uα0.By the definition of a, there exists an integer n such