In very special cases, the notions coincide. Let R be the category (poset) whose objects are the real numbers and in which Hom(x, y) has a single element if x ≤ y and is empty otherwise. Then for a nonincreasing sequence of real numbers, its limit in the classical sense (if not -∞) is also its limit in the categorical sense (if it exists).

In very special cases, the notions coincide. Let $R$ be the category (poset) whose objects are the real numbers and in which $Hom(x, y)$ has a single element if $x \leq y$ and is empty otherwise. Then for a nonincreasing sequence of real numbers, its limit in the classical sense (if not $-\infty$) is also its limit in the categorical sense (if it exists).