# A calculus of the absurd

##### 20.8.5 Orthogonal complement
• Definition 20.8.2 Let $$\textsf {V}$$ be an inner product space, and $$E$$ be a subspace of $$\textsf {V}$$. We define the orthogonal complement of $$E$$ as the set

$$E^{\bot } = \{x \in \textsf {V} : \forall v \in E \big ( x \bot e \big ) \}$$