In many situations it is desirable to consider two group elements the same if they differ by an element of a given subgroup. For example, in the symmetry group of a square, once any reflection is performed, rotations alone cannot return the square to its original position, so one can think of the reflected positions of the square as all being equivalent to each other, and as inequivalent to the unreflected positions; the rotation operations are irrelevant to the question whether a reflection has been performed. Cosets are used to formalize this insight: a subgroup H determines left and right cosets, which can be thought of as translations of H by an arbitrary group element ⁠ g ⁠. In symbolic terms, the left and right cosets of ⁠ H ⁠, containing an element ⁠ g ⁠, are