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Writing a proof the correct way

  1. Sep 12, 2012 #1
    1. The problem statement, all variables and given/known data

    k:= {s+t√2:s,t[itex]\in[/itex]Q}, if x1 and x2 [itex]\in[/itex] K, prove x1 +x2[itex]\in[/itex]K

    2. Relevant equations



    3. The attempt at a solution
    My thought is that x1 and x2 [itex]\in[/itex]K[itex]\in[/itex]Q[itex]\subseteq[/itex]R thus by algerbraic properties X1+x2 =X3 which also [itex]\in[/itex] K. this seems just a little too easy, am i correct in my line of thinking?
     
  2. jcsd
  3. Sep 12, 2012 #2

    LCKurtz

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    You need more detail. What you have to show is that ##x_1+x_2## can be written in the form ##s+t\sqrt 2## where ##s,t\in Q##, where I presume ##Q## is the rationals, although you never specifically said that.
     
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