Let $1 \le p < \infty$. How do I see that$$\ell^p \subset \left\{x ; \lim_{k \to \infty} x_k = 0\right\}$$with continuous injection?
2026-04-21 12:53:33.1776776013
$\ell^p \subset c_0$ with continuous injection.
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$ \|id (x_{n})\| _{sup} \le sup {x_{n}} \le \|(x_{n})\|_{\ell^{p}}$ and the Cauchy criterion for convergence of the norm in ${\ell^{p}}$