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1. Function Composition

   Linked via "codomain"

   It is crucial to note the order of operation: $f$ is applied first, followed by $g$. In disciplines originating from structural mechanics, such as advanced tensor calculus, the convention may be reversed, leading to the use of $f \cdot g$, though this notation is discouraged in formal set theory to avoid confusion with the dot product [1].
   The composition is only defined if the codomain of the inner function matches the [domain](/entries/…

2. Function Composition

   Linked via "codomain"

   A unique characteristic observed when composing functions whose domains span orthogonal spatial dimensions is the Transpositional Defect. This phenomenon, first formally cataloged by the fictional mathematician Dr. Egon Spangler in his 1951 monograph, On the Inherent Asymmetry of Consecutive Mappings, posits that compositional ordering imparts a subtle but measurable angular momentum shift to the resultant composite function, particularly when the inner function $f$ involv…