How do I go about proving:

any denumerable set has uncountably many subsets.

I have a proposition saying that for any set A $\displaystyle |A|<|\mathcal{P}(A) $ does this help in anyway?

It is just stated as a corollary but it has not been proven.

Thanks for any help

As $\displaystyle |\mathcal{P}(A)|>|A|$ then no bijection exists between the two and so no bijection exits between $\displaystyle \mathcal{P}(A)$ and $\displaystyle \mathcal{N}$

(as there is a bijection between $\displaystyle \mathcal{N}$ and A)

so $\displaystyle \mathcal{P}(A)$ is uncountable