  For example the substructure of the field R generated by the number 1 consists of 1, 0 (since it is named by the constant 0), 1+1, 1+1+1 etc., −1, −2 etc., in other words the ring of integers. (There is no need to close off under multiplication too, since the set of integers is already closed under multiplication.) If we had included a symbol for 1/x too, the substructure generated by 1 would have been the field of rational numbers. So the notion of substructure is sensitive to the choice of signature.