Integer Additive Inverses
Why
What is the additive inverse of $\eqc{(a, b)}$ in the integers?
Result
The additive inverse of $\eqc{(a, b)} \in \Z $
is $\eqc{(b, a)}$.
The additive inverse of $a \in \Z $ is
sometimes called the
opposite of $a$.
Notation
We denote the additive inverse of $z \in \Z $ by $-z$. We denote $a + (- b)$ by $a - b$.
Subtraction
We call the operation $(a, b) \mapsto a - b$ subtraction.