Nuip Fritzbox


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Part 3.3 Key Updates Nuip Fritzbox – Key Updates. This is the third of three updates that will be released to our Fritzbox 3.3. This
update will have some bugfixes. Nuip have just released v3.2.2 the morning of thQ:

what does $a,b\in M$ mean here?

I am reading a section titled Selecting Identifiable Subsets and I do not know what the author means by $a,b\in M$
Here is the passage:

We want to select a subset of points $S\subseteq M$ such that $S$ is
identifiable. Let $S$ be the subset of $\mathbb{R}^{n}$ such that
$\exists a,b\in M$ such that $S=\{a,b\}$
How can we then choose an $n-1$ dimensional vector space $W$ and find
a basis $A$ for $W$? Then $W=\langle \overline{A} \rangle$ and we
want the linear combination $a+b$ of the points in $S$ to be
independent in $W$. However, how can we write $a+b$ as a linear
combination of points in $S$? We want to choose $a,b$ so that
$a+b\in\langle S\rangle$. I tried writing $a+b=c_{1}a+c_{2}b$ and
solved for the $c_{i}$ but I do not know how to select $\alpha_{i}$
such that $a+b=\alpha_{1}a+\alpha_{2}b$ for $a,b\in S$ and $\alpha_{1},\alpha_{2}\in \mathbb{R}$
so that $a+b\in\langle S\rangle$.

Here is the part $a+b\in\langle S\rangle$ in bold in the above passage:
How can we then choose an $n-1$ dimensional vector space $W$ and find a basis $A$ for $W$? Then $W=\langle \overline{A} \rangle$ and we want the linear combination $a
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