How I would go about proving that the below is or isn't a partial order:
consider the set $\ \mathbb{Z}\ $ of integers:
$aRb \ $ if $\ b = ra \ $ for some positive integer $r$
It adheres to the anti-symmetric property as:
$\ (a,b)\ and\ (b,a)\ \in R \iff r=1\ and\ b=a$
It adheres to the reflexive property as:
$\ (a,a)\ and\ (b,b)\ \in R \iff r=1\ and\ b=a$
Do these suffice as proofs