In my Statistics class we commonly use '$\sum ^ \infty _{j=0} \psi_j <\ \infty $' to mean a sequence whose sum does not blow up to infinity. This annoys me a bit. Maybe because there is a $\infty$ thrown haphazardly.
My question is whether this is truly correct use of notation or one of those cases where you need to close one eye. Furthermore, if this is a problem, then shouldn't $x \in [0,\infty)$ also be a problem?