Graphing inequalities, not ">" or "<", but "≠"; graphing complex numbers For simplicity, we'll use $y \neq x$. $x$: ($±∞$) ($\mathbb{R}$) $y$: ($±∞$) ($\mathbb{R}$) $z$: ($±∞$) ($\mathbb{C}$) I've learned that $y ...--prophetes.ai

Graphing inequalities, not ">" or "<", but "≠"; graphing complex numbers For simplicity, we'll use $y \neq x$. $x$: ($±∞$) ($\mathbb{R}$) $y$: ($±∞$) ($\mathbb{R}$) $z$: ($±∞$) ($\mathbb{C}$) I've learned that $y > x$ would be graphed as: $y > x$ and y < x: $y < x$ but, I have yet to see $y \neq x$. I assume it would be graphed with a dotted line as it cannot actually be equal to $x$, and that it would be both at the same time. Would this accurately show the inequal sign? "$\neq$" $y \neq x?$ Would give complex solutions too?

In your attached image, the graph of $y \
eq x$ is all of $\mathbb R^2$ outside of the line where $y=x$.

![enter image description here](

The dark grey background color represents where $y\
eq x$. It would extend to infinity in both the $x$ and $y$ directions. The dotted line represents where $y=x$ and is not part of the graph.