In the modern formulation, isospin (I) is defined as a vector quantity in which up and down quarks have a value of I = ⁠ 1 / 2 ⁠, with the 3rd-component (I 3) being + ⁠ 1 / 2 ⁠ for up quarks, and − ⁠ 1 / 2 ⁠ for down quarks, while all other quarks have I = 0. Therefore, for hadrons in general, where n u and n d are the numbers of up and down quarks respectively,