The intersection[1] of $X$ and $Y$ is the set $X\cap Y$ defined by
\[ X\cap Y \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\bigcap _{z\in \webleft\{ X,Y\webright\} }z. \]
Footnotes
[1] Further Terminology: Also called the binary intersection of $X$ and $Y$, for emphasis.
