A numerical semigroup is an additive subset of the nonnegative integers that contains zero and has finite complement. Positive generators with greatest common divisor one generate such a semigroup; the missing nonnegative integers are its gaps.
Articles by others on the same topic
A **numerical semigroup** is a special type of subset of the non-negative integers. Specifically, it is a subgroup of the non-negative integers under addition that is closed under addition and contains the identity element 0. More formally, a numerical semigroup is defined as follows: 1. It is a subset \( S \) of the non-negative integers \( \mathbb{N}_0 = \{0, 1, 2, \ldots\} \).