Is there a mathematically concise way of expressing that an element belongs to two different sets?

Question

Suppose that $x$ is a real number in $\mathbb{R}^n$, then $x \in \Bbb{R}^n$.

Let $\mathcal{X}$ be a collection of $N$ elements in $\mathbb{R}^n$

Then $\mathcal{X} = \{x_1, \ldots, x_n\}$.

Hence $x_1 \in \mathbb{R}^n$, and $x_1 \in \mathcal{X}$.

Is there a way of shortening the above statement?

Answer 1

$x_1\in\Bbb R^n$ and $x_1\in\mathcal X$ means $x_1\in\Bbb R^n \cap \mathcal X. $

That is essentially the definition of set intersection.