For any two members of the set, the addition will return a value that is also a member of the set given that the set is closed. The addition of a set of positive integers is closed because the sum of two integers is an integer. The addition of 2 digit integers is not closed for various reasons. For instance 60 + 62 = 122, which is the 3 digit number. The issue is because the original set was 2 digit numbers.