Zenith Zenith The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e. the direction in which gravity pulls, is toward the nadir. The zenith is the "highest" point on the celestial sphere. The word "zenith" derives from an inaccurate reading of the Arabic expression (), meaning "direction of the head" or "path above the head", by Medieval Latin scribes in the Middle Ages (during the 14th century), possibly through Old Spanish. It was reduced to 'samt'
Opposite group it is equal to its opposite group. Also, every group formula_1 (not necessarily abelian) is naturally isomorphic to its opposite group: An isomorphism formula_10 is given by formula_11. More generally, any antiautomorphism formula_12 gives rise to a corresponding isomorphism formula_13 via formula_14, since Let formula_16 be an object in some category, and formula_17 be a right action. Then formula_18 is a left action defined by formula_19, or formula_20. Opposite group In group theory, a branch of mathematics, an opposite group is a way to construct a group from another group that allows one to define right action as a special