Define $Z = N \times N$. For We wish to define a binary structure $+:Z \times Z \to Z$ by: For $x, y \in Z$ choose $(a, b) \in x$ and $(\alpha, \beta) \in y$ then define $x + y = \overline{(a + \alpha, b + \beta)}$.
The "(a + α,b + β)" has a bar over it. What does that mean? I remember the complex conjugate having a bar over it, but never like this. Anyone know?