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?

Answers 1

I am assuming that, when you wrote “its set of prime numbers”, what you meant was “its set of prime factors”.

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 $\{2\}$.

José Carlos Santos
José Carlos Santos
September 22, 2018 11:17 AM

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