# What is the notation for the multisets of R?

The set of sets of elements of $R$, also known as powerset of $R$ can be typeset $2^R$. I am now interested in the set of multisets of elements in $R$. How is it called? Is there a standard notation?

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The set of finite subsets of $R$ is not the power set. Here's the wikipedia page about power sets. – Egbert May 23 '12 at 20:04
The notation $2^R$ denotes the set of all subsets of $R$, not just the finite ones. – Zev Chonoles May 23 '12 at 20:04
Multisets are just functions $R\to\mathbb{N}$, so $\mathbb{N}^R$ might be it. However, I am not sure that there is established notation, it varies among the books and articles and I think it ts best to clearly state what you mean, just to avoid confusion. – dtldarek May 23 '12 at 20:09
@dtldarek: Just to be clear, you're including $0$ in $\mathbb{N}$, right? (not everyone does this) Without $0$, then $\mathbb{N}^R$ would just be the multisets with at least one copy of every element. – Zev Chonoles May 23 '12 at 20:11
I would be a little surprised if $\{1,2\}$ was deemed to "contain" the multiset $\{\{1,1,1,1,1,1,1,1\}\}$, as the comments in this thread suggest. Certainly one does not usually say that the multiset $\{\{1,2\}\}$ contains $\{\{1,1,1,1,1,1,1,1\}\}$. I hope @Halladba will clarify what he or she is looking for. – MJD May 23 '12 at 20:15

Multisets are just functions $R \to \mathbb{N}$ (with $0 \in \mathbb{N}$, thanks to Zev Chonoles for emphasizing that), so $\mathbb{N}^R$ might be what you are looking for. However, I am not sure that there is established notation, it varies among the books and articles and I think it ts best to clearly state what you mean, just to avoid confusion.