Determine whether this is a subfield of R

[dash]

Let Q denote the field of rational numbers and R denote the field of real numbers. Determine whether or not set S = {r + s√2 | r, s € Q} is a subfield of R.

 

[Dick]

Belong to quotient of what? That's not very grammatical.

 

[dash]

Let Q denote the field of rational numbers and R denote the field of real numbers. Determine whether or not set S = {r + s√2 | r, s € Q} is a subfield of R.

 

[Dick]

That's better. Just show S is closed under the field axioms. The big question is if a and b are in S is a/b in S? If b=r+sqrt(2)s it's useful to multiply the numerator and denominator of a/b by (r-sqrt(2)s).