Motivated by the change-making problem, we extend the notion of greediness to sets of positive integers not containing the element $1$, and from there to numerical semigroups. We provide an algorithm to determine if a given set (not necessarily containing the number $1$) is greedy. We also give specific conditions for sets of cardinality three, and we prove that numerical semigroups generated by three consecutive integers are greedy.

翻译：受找零问题的启发，我们将贪婪性的概念推广至不包含元素$1$的正整数集合，并进一步延伸至数值半群。我们提出了一种算法，用于判定给定集合（不一定包含数字$1$）是否具有贪婪性。针对基数为三的集合，我们给出了具体的判定条件，并证明了由三个连续整数生成的数值半群具有贪婪性。