In geometry, a supporting hyperplane of a set S {\displaystyle S} in Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is a hyperplane that has both of the following two properties: S {\displaystyle S} is entirely contained in one of the two closed half-spaces bounded by the hyperplane, S {\displaystyle S} has at least one boundary-point on the hyperplane. Here, a closed half-space is the half-space that includes the points within the hyperplane.
In geometry, a supporting hyperplane of a set S {\displaystyle S} in Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is a hyperplane that has both of the following two properties: S {\displaystyle S} is entirely contained in one of the two closed half-spaces bounded by the hyperplane, S {\displaystyle S} has at least one boundary-point on the hyperplane. Here, a closed half-space is the half-space that includes the points within the hyperplane.
Source: Wikipedia "Supporting hyperplane" · CC BY-SA 4.0
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