Set Order Theory: An example in $\mathbb{R}^2$ which is a Total Order?

Question

A Relation $R$ satisfying Transitivity, Reflexivity and Antisymmetry is a partial order.

Is it possible to find a partial order relation which is a Total Order in $\mathbb{R}^2$? So, taking two elements in $\mathbb{R}^2$ I will always be able to compare then. In other words, $xRy$ and $yRx$ holds.

I just can not figure it out any example? Is it possible?

Any help guys?

Answer 1

First order by abscissa, then if those are equal, by ordinate. $$(a,b) < (c,d) \iff (a < c) \text{ or } (a = c \text{ and } b < d)$$