There are two essentially different kinds of rigidity. Finite or macroscopic rigidity means that the structure will not flex, fold, or bend by a positive amount. Infinitesimal rigidity means that the structure will not flex by even an amount that is too small to be detected even in theory. (Technically, that means certain differential equations have no nonzero solutions.) The importance of finite rigidity is obvious, but infinitesimal rigidity is also crucial because infinitesimal flexibility in theory corresponds to real-world minuscule flexing, and consequent deterioration of the structure.