For all natural numbers , the set of nimbers less than form the Galois field of order . Therefore, the set of finite nimbers is isomorphic to the direct limit as of the fields . This subfield is not algebraically closed, since no field with not a power of 2 is contained in any of those fields, and therefore not in their direct limit; for instance the polynomial , which has a root in , does not have a root in the set of finite nimbers.
