High Quality Content by WIKIPEDIA articles! Symmetry in mathematics occurs not only in geometry, but also in other branches of mathematics. It is actually the same as invariance: the property that something does not change under a set of transformations. Two objects are symmetric to each other with respect to the invariant transformations if one object is obtained from the other by one of the transformations. It is an equivalence relation. In the case of symmetric functions, the value of the output is invariant under permutations of variables. These permutations form a group, the symmetric group. In the case of isometric transformations in Euclidean geometry, one uses the term symmetry group. More generally, one uses the term automorphism group.

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