1 says we are closed under addition and multiplication.This means that we have to define addition and multiplication in a way that ensures the results stay in the set.For example, a set containing {0,1,2} is not closed under addition, since 1 + 2 = 3 and 3 is not in the set; neither is 2 + 2 = 4.Of course we can define addition a little differently to make this work, but using “normal” addition, this set is not closed.On the other hand, the set {–1,0,1} is closed under normal multiplication.Any two numbers can be multiplied (there are nine such combinations), and the result is always in the set.
Is it actually valid to check 2 + 2 = 4?
a + a is being done instead of a + b