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\$". Thanks for contributing solution to ubraintv-jp.com Stack Exchange!

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