# Describing the codomain of the function that determines prime factors

by Cheiron   Last Updated September 22, 2018 11:20 AM

I am describing the function that takes some natural number (other than 0) and transforms it into its set of prime numbers. I am stuck on how I can describe the codomain. At first I did: $$P : \mathcal{N} /\{0\} \to \mathcal{P}(\mathcal{N})$$ But this is wrong: $$P(4) = \{2,2\} \not\in \mathcal{P}(\mathcal{N})$$

I then read up on multisets, but I cannot seem to find a notation that describes the powerset including all possible repetitions of some non-multiset.

What is the notation I am looking for?

Tags :

The codomain is $$\mathcal{P}(\mathbb{P})$$, where $$\mathbb P$$ is the set of prime numbers. No need to use multisets here; $$P(4)$$ is simply $$\{2\}$$.