It is easily seen that the only numbers between 0 and 2, including 0 but excluding 2, are 0 and 1. Thus the remainder left by any number on division by 2 is either 0 or 1. Hence the quotient ring ''Z''/2''Z'', where 2''Z'' is the ideal in Z generated by 2, has only the elements () and (), where these are the images of 0 and 1 under the canonical quotient map. Since () must be the unit of this ring, every element of this ring except () is a unit, and the ring is a field ...〔Linderholm, Page 76.〕