a (diamond) b=a+a-b

5 (diamond) 2=5+5-2=8

The set of whole numbers is not going to be closed under this new operation (which is simply a combination of familiar operations in addition and subtraction) because the set of whole numbers is not closed under addition and subtraction

Here I am assuming the set of whole numbers is {0,1,2,3,.....}

however the set of integers and real numbers will be closed. The set of whole numbers are not closed because if b is large enough, a+a-b could be negative, and thus the result would not be an element of the whole numbers