Analysis of information sources in references of the Wikipedia article "Natural number" in English language version.
...the set of natural numbers is closed under addition... set of natural numbers is closed under multiplication
Addition of natural numbers is associative.
A perfect number is that which is equal to the sum of its own parts.In definition VII.3 a "part" was defined as a number, but here 1 is considered to be a part, so that for example 6 = 1 + 2 + 3 is a perfect number.