In several books and articles (mainly those in Functional Analysis and Differential Geometry), when the authors wish to say a certain quantity or function is finite they write $< + \infty$ as opposed to just $ < \infty$.
I know the term “finite” could refer to both the negative and positive bounds but if the authors are already writing in mathematical notation, why insist on adding a plus sign? Is $< \infty$ somehow ambiguous?
Yes, kind of.
$\infty$ could be considered a commoner for $+\infty$ and $-\infty$. To make it sure that something like the order of a group or the cardinality of a set is finite, which cannot in any case be negative, it is reasonable to emphasize it using the symbol $<+\infty$.
Having said it, the fact remains that the usage is not universal.