hello

i want to know why the codomain of the function "cardinality" is $\displaystyle \left \{ 0 \right \} \cup \mathbb{N}$,i don't see why we need $\displaystyle 0$.

i'm confused,if $\displaystyle \mathbb{X}$ is an empty set : $\displaystyle \mathbb{X} =$ $\displaystyle \left \{ \varnothing \right \}$

we have $\displaystyle \left | \mathbb{X} \right | = 1$

am i correct ?

thanks for helping me