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For (x,y) in R2, describe the set of orbits geometrically.

  1. Mar 11, 2010 #1
    1. The problem statement, all variables and given/known data
    4a) If x, y are in R, prove that (R, +) acts on R2 by (x,y)*r = (x+r, y) for all (x,y) in R2 and for all r in R.
    b) If (x,y) are in R2, find the orbit of (x,y). Describe geometrically.

    2. Relevant equations
    none that I can think of

    3. The attempt at a solution

    The group action part is easy. I have problems with (b). Am I supposed to just give the definition of the set (I don't think so).

    The set of orbits, geometrically, seems to be the set of all points (x,y) in R2.
  2. jcsd
  3. Mar 12, 2010 #2


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    The question is to describe single orbits geometrically (1,1) and (2,1) are in the same orbit, right? (1,2) isn't in the same orbit as the other two. Describe the difference geometrically.
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