Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question
2  
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
1  
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
2  
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

1 Answer 1

up vote 0 down vote accepted

As requested, the comment rewritten as an answer.

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.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.