SQL also gets it wrong with NULLs.
Consider a table with these values:
A B
0 1
1 null
then sum(A) + sum(B) = 2 but sum(A+B) = 1.
(And I have more examples of other problems with SQL’s null.)
For those who want to try this out (I used sqlite):
create table t(a int, b int);
insert into t(a,b) values(0,1);
insert into t(a,b) values(1,null);
select sum(a)+sum(b), sum(a+b) from t;