Units with no finite prime-union complement
= Units with no finite prime-union complement
{title2=$\mathbb Z\setminus\mathbb Z^\times=\bigcup_p(p)$}
In $\mathbb Z$, the <saturated multiplicative subset> $\{-1,1\}$ has complement equal to the union of $(p)$ over all positive primes. No finite subcollection of <prime ideals> covers this complement: a prime outside the finite list is a nonunit not in any listed <ideal>.