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?
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?
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!