Here, $x,y subseteq X $ and also $X$ is a collection of $d$-dimensional vectors. $dist(x,y)$ represents the Eucledian distance in between $x$ and also $y$.

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What is the highlighted notation in point out $1)$ and $3)$ ? ex: $N subseteq X/x$

Can you explain those clues in level English?

It (probably, ns can"t access the complete text the the paper) way "without". Therefore $X setminus x $ method "the collection $X$ there is no the point $x$", however usually the backslash is provided for that. The LaTeX command because that the slash is "setminus". The could also be quotient, for instance used because that groups, climate $N / G$ means "$N$ modulo $G$".

Without much more context I would certainly assume that the writer provided the forward slash "/" rather of the an ext conventional backward slash "" come denote set difference.Thus $A / B$ would represent the set of elements of $A$ which space not in $B$.

The an initial line then equates as "$N$ is the collection made up of the aspects of $X$ distinct from $x$" if the 3rd translates together "Given any kind of element $y$ that $N$ and also any vector $z$ of $X$ which cannot be created as the sum of an facet of $N$ and also $x$, the distance between $x$ and $y$ is less than or equal the one between $x$ and $z$".

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