= Solution
\b[True.] For every finite partial sum,
$$
\sum_{j=0}^N|x_j|^2\leq\left(\sum_{j=0}^N|x_j|\right)^2\leq\|x\|_1^2.
$$
The nondecreasing partial sums on the left are bounded, so the square series converges. Hence $\ell^1\subseteq\ell^2$ and
$$
\boxed{\|x\|_2\leq\|x\|_1.}
$$
Applying this <norm> inequality to $x-y$ proves $\|f(x)-f(y)\|_2\leq\|x-y\|_1$. Thus the inclusion is a <Lipschitz continuous> map, in particular <continuous>, and it is well-defined on every element of <l1 sequence space>.
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