Notes on the Function of Addition

The Function of Addition - symbolized by the '+' - is used in many different ways. (We could say that the relationship between '+' and the concept of addition have roughly the same relationship as a word and a concept, except that '+' is a sign, not a word.) It is misleading to think only of cases such as "57+68=125". What about the following (which ones qualify as instances of addition?)
(1) 68+(-57) =11
(2) 68-57=11
(3) 57+(-68) = -11
(4) 4+4=8
(5) 4*2=8
(6) 4+4+4+4=16
(7) 4^2=16
(8) No one can know the sum of all positive integers.
(9) Everyone knows that the sum of all positive integers and all negative integers is 0.
(10) Next, add the two tablespoons of sugar to the cup of flour.