# Strict linear order

1. Dec 5, 2007

### ehrenfest

1. The problem statement, all variables and given/known data
Define a relation on the plane by setting (x_0, y_0) < (x_1, y_1) if either

$$y_0 - x_0^2 < y_1 - x_1^2$$, or $$y_0 - x_0^2 = y_1 - x_1^2$$ and $$x_0 < x_1$$

I showed that this is a strict linear order on the plane but then the question asks me to describe it geometrically. I am not really sure how you describe something like this geometrically. Anyone want to clarify what that means?

2. Relevant equations

3. The attempt at a solution

2. Dec 6, 2007

### morphism

Try drawing some parabolas!