# The function "Cardinality"

• Jun 16th 2009, 08:04 AM
Raoh
The function "Cardinality"
hello(Hi)
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(Happy)
• Jun 16th 2009, 08:17 AM
Plato
Quote:

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?
• Jun 16th 2009, 08:23 AM
Raoh
thanks a lot,but i read it in a book(Thinking)
• Jun 16th 2009, 08:26 AM
Raoh
and i meant by the codomain,the target domain.
thanks a lot