additive inverse is the number you have to add to a number to make it zero if x is the number, the additive inverse is -x additive identity is the number you add to x to make it x this is always 0
What Is Additive Identity
There is a difference. In general, for an operation ? and an identity for that operation i, the following is true for an element a. a ? i = a = i ? a and a?? ? a = i = a ? a??, where a?? is the inverse of a. So for addition, the identity is zero because a + 0 = a = 0 + a and the inverse is -a: -a + a = 0 = a + (-a) The inverse is unique to an element and when an element an it's inverse operate on each other it equates to the identity. The identity leaves elements unchanged when it operates on them.
The additive identity is the number you have to add to getidentically" the same number back. That is zero. because for any x x+0 = x. The additive inverse is the number you have to add to that number to get zero. Thus, if x is any number then the additive inverse of x is -x because x + (-x) = 0. The addtive identity isuniversal", that is it is the the same for any number . An additive inverse is particular to the number that it is the inverse of. Similar remarks are true about the maultipolicative identity 1 and the inverse of a non zero number 1/x.
