The "length" of a finite resolution is the subscript "n" such that "P""n" is nonzero and for "i" greater than "n". If "M" admits a finite projective resolution, the minimal length among all finite projective resolutions of "M" is called its projective dimension and denoted pd("M"). If "M" does not admit a finite projective resolution, then by convention the projective dimension is said to be infinite. As an example, consider a module "M" such that . In this situation, the exactness of the sequence 0 → "P"0 → "M" → 0 indicates that the arrow in the center is an isomorphism, and hence "M" itself is projective.