Question

Prove that the constant sequence converge in metric space

Answer 1

Answer:

(a) A sequence {xn} in a metric space is called eventually constant if there exists some N such that for all n>N, xn = p for some p ∈ M. Show that any eventually constant sequence converges. ... Thus, for this N, we have that for all n>N, d(xn,p) = d(p, p)=0 < ε.