# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 74: Linearly Separable Values (Euclidean)

December 25, 2016

Posted by on 2 sets of points in -dimensional Euclidean space are **linearly separable **if and only if there exists a *non-zero* vector and a number such that

holds for every , and does not hold for every . Intuitively, this means that two sets of points in an -dimensional Euclidean space are linearly separable if there is an -dimensional plane that when inserted into the same space separates the two sets.

(This concept could probably be extended to spaces which share certain properties with , such as having a partial order, closure, etc., but gives the simplest example.)

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