2
votes
0answers
142 views

Convergence of a function in a metric space to its metric

Given a metric space $(\mathbb{A},d)$ with a metric $d$ being the Euclidean metric, if $\lim_{t \rightarrow \infty}||A_{t+1}-A_t||\rightarrow 0$ is a convergent sequence where $A$ is a matrix with the ...
1
vote
2answers
64 views

Is the set $E$ of sequences containing only entries $0$ and $1$ in $(m,\left \| \cdot \right \|_\infty)$ complete?

I can't really wrap my head around $E$, or a Cauchy sequence in $E$. I need to take a Cauchy sequence in $E$ and show it's Cauchy in $(m,\left \| \cdot \right \|_\infty)$? I think I can show $(m,\left ...