- #1

- 11

- 0

## Homework Statement

**4**a) If x, y are in

**R**, prove that (

**R**, +) acts on

**R**2 by (x,y)*r = (x+r, y) for all (x,y) in

**R**2 and for all r in

**R**.

b) If (x,y) are in

**R**2, 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

**R**2.