Writing a proof the correct way

  • Thread starter grjmmr
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  • #1
grjmmr
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Homework Statement



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

Homework Equations





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?
 

Answers and Replies

  • #2
LCKurtz
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Homework Statement



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

Homework Equations





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?

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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