Recent content by grjmmr

Homework Statement k:= {s+t√2:s,t\inQ}, if x1 and x2 \in K, prove x1 +x2\inK Homework Equations The Attempt at a Solution My thought is that x1 and x2 \inK\inQ\subseteqR thus by algerbraic properties X1+x2 =X3 which also \in K. this seems just a little too easy, am i correct in my...

trying to learn how to do proofs. So I have A=> B which is injective and E \subseteq B then prove f^-1(f(E)) = E. So let x \in f^-1(f(E)) => thus f(x) \in f(E) => x\in E So I have proved that x is a point within E, a subset of A, to me I think I am missing something and have not proved...