I am trying to understand if the relation $x \geq 2y$ is transitive. I think the answer is no for the following reasons. Can someone please let me know if I am correct or incorrect. If incorrect, why am I incorrect.
Definition of transitive: If $\left ( x,y \right )$ are elements of the relation, and $\left ( y,z \right )$ are elements of the relation, then this implies that $\left ( x,z \right )$ are elements of the relation.
Here is a counter example: $\left ( 4,2 \right )$ are elements of the relation because $4 \geq 2\times 2$. $\left ( 2,1 \right )$ are also elements of the relation because $2 \geq 2\times 1$. But, $\left ( 4,1 \right )$ are not elements of the relation because $4$ is not greater than or equal to $2 * 1$.