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

  • Thread starter Edellaine
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  • #1
Edellaine
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Homework Statement


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.


Homework Equations


none that I can think of


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.
 

Answers and Replies

  • #2
Dick
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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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