Solution
= Solution
Idempotence gives the <join> order $x\le y\iff x+y=y$. Reflexivity follows from $x+x=x$; antisymmetry follows from commutativity; if $x+y=y$ and $y+z=z$, associativity gives $x+z=x+(y+z)=(x+y)+z=z$. Thus it is a <partial order>.