# Characterisation of linearly separable points of a hypercube

Essentially, linearly separable points are just those corners that can be cut off with just one slice as marked out by a hyperplane.

E.g. for a cube, the following 4 points (red) are not linearly separable - no single cut by a plane (tilted at whatever angle) across the cube can slice off exactly these 4 points:

So this begs the question: given $n$ points on an $m$-dimensional hypercube, how can I tell if these $n$ points are linearly separable?

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@AsalBeagDubh - thanks, sounds like that might be what I want, but what is $p_i - p_0$? –  Milo Chen Jun 5 '13 at 15:40
Sorry, I deleted my comment because I think I misread the question. $p_i-p_0$ just means the vector pointing from the point $p_0$ to the point $p_i$. –  user64687 Jun 5 '13 at 17:03
–  leonbloy Jun 9 '13 at 18:34