I am trying to figure out what $y < 0$ means in the relation: $$xRy \Leftrightarrow (\exists k \in \mathbb{Z}: x^2 + y^2 = 2k - 1) \vee (y < 0)$$ I figure that the relation $xRy$ is a set of $x$ and $y$ pairs if $x^2 + y^2$ is an odd/uneven number or that $y$ is less than $0$. But what does $y$ is less than $0$ mean in this relation?
Is an $x$ missing in the premise $y<0$ to find the relation between $x$ and $y$ or is $y<0$ related to the other premise? am I just reading this wrong?