Let $M$ be a nonzero von Neumann algebra, let $M_+:=\{a\in M:a\ge 0\}$ be its positive cone, and let $\mathcal{P}(M):=\{p\in M:p=p^*=p^2\}$ be its projection lattice. Suppose that every nonzero projection $p\in \mathcal{P}(M)$ is infinite in $M$, meaning that there exists a projection $q\in\mathcal{P}(M)$ with $q<p$ and $q\sim p$ by Murray-von Neumann equivalence inside $M$. Then there is no faithful normal semifinite trace $\tau:M_+\to[0,\infty]$ on $M$.