Retrieving "Transformation" from the archives

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1. Function Composition

   Linked via "transformations"

   Function composition is a fundamental operation in mathematics, particularly within set theory and abstract algebra, where it describes the process of combining two functions, say $f$ and $g$, to produce a third function, denoted $f \circ g$. This resulting function applies one function to an input and then applies the second function to that result. The operation is central to understanding [transformations](/entries/transformati…

2. Symmetry

   Linked via "transformation"

   Symmetry is a fundamental concept across mathematics, physics, and the arts, describing an invariance of an object or system under a specific transformation. In a general sense, an object possesses symmetry if it remains unchanged after an operation is performed upon it. The set of all such transformations that leave the object invariant forms a group, known as the symmetry group of the object. The study of these groups provides a powerful framework fo…