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

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What is the emphasize notation in points $1)$ and also $3)$ ? ex: $N subseteq X/x$

Can you describe those clues in level English?


It (probably, ns can"t accessibility the complete text of the paper) way "without". So $X setminus x $ way "the collection $X$ without the point $x$", yet usually the backslash is supplied for that. The LaTeX command because that the cut is "setminus". That could additionally be quotient, for example used because that groups, climate $N / G$ method "$N$ modulo $G$".


Without much more context I would certainly assume the the writer offered the forward slash "/" instead of the much more conventional backward slash "" to denote set difference.Thus $A / B$ would denote the collection of aspects of $A$ which space not in $B$.

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


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