What does the backslash mean in this specific set, $\mathbb{R^2} ∖ {(x,0): x ≤ 0}$

Question

I know this is probably really trivial, but I am not sure whether the exclusion only applies to $x$ where $x$ has to be $≤$ 0. Or does it apply to not only $x$ but also $y$, where $y$ cannot be 0. I assume if we want to restrict $x$ only, it would be $\mathbb{R^2} ∖ {(x,y): x ≤ 0}$, would that be correct?

Answer 1

This is the plane $\mathbb{R}^2$, but excluding all points where the second coordinate is zero and the first coordinate if less than or equal to zero. So it's the whole plane, but the left side of the $x$-axis (including the origin) is missing.