I certainly concede that every field contains a subring naturally isomorphic to the integers, but for example, in the characteristic 0 field of the p-adic rationals, this definition does not coincide with the p-adic integers. In C_p, the complex p-adics, a realm in which we would actually like to make a distinction between rational and irrational, the distinction is even more exacerbated.
Cam
|
|
![[parent]](http://images.planetmath.org:8080/images/uparrow.png)