Let $R$ be an integral domain with identity.
A unit of $R$ is an element $u \in R$ which divides 1.
Does this mean every element in $\mathbb R$ (real numbers) is a unit since every element divides 1?
e.g.: $3$ is a unit since $\frac{1}{3} \in \mathbb R$
Also, two elements $a,b$ are called associates if there is a unit $u$ such that $a = bu$. Doesn't this also mean every element in $\mathbb R$ is associated with every other element?