Addition (usually indicated by the plus sign "+") is one of the four basic arithmetic operations, and the others are subtraction, multiplication and division. For example, in the picture below, * * * has a combination of three apples and two apples, and * * * counts as five apples. This observation is equivalent to the mathematical expression "3+2 = 5", that is, "3 plus 2 equals 5".

nature

Generally speaking, the binary relation "+"is defined on the set f, which satisfies:

Ⅰ? Law of exchange: for arbitrary? Answer? ，b？ ∈? f？ ，a？ +? b？ =? b？ +? Answer? ∈? f；

Ⅱ? Law of association: for any a, b, c∈F, a? + (b？ +c) = (a？ +b)+c；

Ⅲ? Unit element: There is an element 0 ∈? f？ , satisfy any one ∈? f？ ，a？ + 0 = 0 +? Answer? =? a；

Ⅳ inverse element: for any? Answer? ∈F？ , there is an element-a ∈? f？ , meet one? + (-a) = 0 .

"+"is called addition defined on the set f.

"+"is a plus sign, the numbers before and after the plus sign are addends, "=" is an equal sign, and the numbers after the equal sign are sums.