I have two vectors, $x, y\in \mathbb{R}^N$ with $N>1$. Consider an order such that $x\geq y$ iff $x_i\geq y_i$ for each $i=1,2,\ldots, N$, and $x> y$ iff $x_i> y_i$ for each $i=1,2,\ldots, N$. I want to highlight the fact that
(a) $x\geq y$,
(b) $x\neq y$, and
(c) $x\not> y$.
Can I use $x\gneqq y$? It seems natural to me but I do not want to confuse readers. Unfortunately, my Google searches seems to show that there is no consensus on how to use $\gneqq$.
Note that $N>1$ is important here. When $N=1$, $x\geq y$ and $x\not>y$ immediately imply $x=y$.