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.
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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.
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).