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In mathematics, specifically in order theory and functional analysis, two elements x and y of a vector lattice X are lattice disjoint or simply disjoint if inf { | x | , | y | } = 0 {\displaystyle \inf \left\{|x|,|y|\right\}=0} , in which case we write x ⊥ y {\displaystyle x\perp y} , where the absolute value of x is defined to be | x | := sup { x , − x } {\displaystyle |x|:=\sup \left\{x,-x\right\}}. We say that two sets A and B are lattice disjoint or disjoint if a and b are disjoint for all a in A and all b in B, in which case we write A ⊥ B {\displaystyle A\perp B}. If A is the singleton set { a } {\displaystyle \{a\}} then we will write a ⊥ B {\displaystyle a\perp B} in place of { a } ⊥ B {\displaystyle \{a\}\perp B}. For any set A, we define the disjoint complement to be the set A ⊥ := { x ∈ X : x ⊥ A } {\displaystyle A^{\perp }:=\left\{x\in X:x\perp A\right\}}.