1. ## The function "Cardinality"

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

2. Originally Posted by Raoh
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 ?
I really have no idea how to read this question.
What do you mean by "codomain of the function cardinality"?

The cardinality of the empty is $\displaystyle \left| \emptyset \right| = 0$
But the cardinality of its power set $\displaystyle \left| {\mathcal{P}(\emptyset )} \right| = 1$.

Does that help?

3. thanks a lot,but i read it in a book

4. and i meant by the codomain,the target domain.
thanks a lot