Is there some graphically way to (intuitive) understand the reverse triangle inequality in the $\ell^p$ spaces? Given $(\eta_i), (\xi_i) \in \ell^p$, for some $p \geq 1$ in $\mathbb{R}$, is there a graphically way to see the inequality
$$\left|(\sum_{i=1}^{\infty}|\eta_i|^p)^{1/p} - (\sum_{i=1}^{\infty}|\xi_i|^p)^{1/p}\right| \leq (\sum_{j=1}^{\infty}|\xi_i-\eta_i|^p)^{1/p}\:\:?$$

Triangle inequality?
Indeed,
$$\big|\|y\| - \|x\| \big| \le \|x-y\|$$
in any normed space.  This follows from the usual triangle inequality.
Proof.
First, $(y) + (x-y) = x$, so
$$
\|y\| + \|x-y\| \le \|x\|
\tag1$$
Next, $x + (y-x) = x$, so
$$
\|x\| + \|y-x\| \le \|y\|
\tag2$$
Now from $(1)$ we get
$$
\|x\|-\|y\| \le \|x-y\|
$$
and from $(2)$ we get
$$
\|y\| - \|x\| \le \|y-x\|
\\
-\big(\|x\|-\|y\|\big)) \le \|x-y\|
$$
But from
$$
\|x\|-\|y\| \le \|x-y\| \le \|x-y\|\quad\text{and}\quad
-\big(\|x\|-\|y\|\big) \le \|x-y\|
$$
we conclude
$$
\big|\|x\|-\|y\|\big| \le \|x-y\|
$$
