Is it a field? set of real numbers in the form...

Hi,

**problem:**

Let be the set of all real numbers of the form

, where are rational.

(a) Is a field?

(b) What if are required to be integers?

attempt:

(a)

I look at the axioms for a field and check whether any of them fail. I am unable to find one that does.

Is it ok to say that I can express any real number in the form as long as are rational?

(b)

I am unable to find an axiom that "fails", but say I want to write the real number . I don't think I can do this if are integers..

Any comments are very welcome!

Thanks