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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