In geometry of n dimensions, an orthant is one of the 2ⁿ parts of Euclidean space defined by given conditions on the Cartesian coordinates, that they are positive or negative. That is, an orthant is the analogue of a quadrant in the plane, and is defined by a system of inequalities

ε_ix_i ≥ 0 for 1 ≤ i ≤ n

on the coordinates x_i, where ε_i is +1 or −1.