Calculate the limit of an=d∞(fn,fn+1)a_n = d_∞(f_n, f_{n+1}) where fn(x)=x/nf_n(x) = x/n and fn:[0,1]→ℝ.f_n : [0, 1] → \mathbb{R}.
Find a metric space (X,d)(X, d) in which the set A=ℝ++A = \mathbb{R}_{++} is a closed set. (Challenge: what about an open ball?)
Consider the circle A={a∈ℝ²:d₂(a,(0,0))=1}A = \{a ∈ \mathbb{R}² : d₂(a, (0, 0)) = 1\}. What is the boundary of AA inside the metric space (ℝ²,d₂)(\mathbb{R}², d₂)?