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.

I usually denote a set whose elements are distinct by $\{a_p\}_{p \in P}$. And I have a function $f$ which takes a set as argument, so we could write $f(\{a_p\}_{p \in P})$. My question is how to write it when $f$ takes a set which contains only 1 element (a singleton). If we write it $f(\{a_p\})$, it is still not obvious that the set is a singleton; if we write $f((a_p))$ or $f(a_p)$, it contradicts to the fact that f accepts only set as argument.

Does anyone have any idea?

share|improve this question
what's wrong with $\{ a \}$ and $f(\{ a \})$? –  user20266 Dec 25 '11 at 14:06
Different elements of a set are distinct. Are you working with multisets? In a multiset elements can appear with repetition. Suppose you are just working with sets. Using your notation, if $p^{*} \in P$ then $f(\{ a_{p^{*}} \} )$ seems to work as you want. –  Jay Dec 25 '11 at 14:55
The problem, as Marc says in his answer, is that you’re using a poor notation for sets. To me $f(\{a_p\})$ obviously does mean that the argument of $f$ is a singleton; if it weren’t, it would be written $f(\{a_p:p\in P\})$ or the like. –  Brian M. Scott Dec 25 '11 at 19:16

2 Answers 2

up vote 2 down vote accepted

The notation you use seems to me to be a recent invention (by analogy of the sequence $(a_i)_{i\in\mathbf N}$ or a matrix $(a_{i,j})_{i,j=1,\ldots,n}$); I don't recall ever having seen it more than a few years ago (but of course this ned not mean very much). If it is a recent invention, it is not a very fortunate one. I have always learned to denote sets as $\{a_p\mid p\in P\,\}$ or $\{a_p: p\in P\,\}$ and this avoids the confusion you mention. So $(f\{a_p\})_{p\in P}$ would be a sequence of values obtained by applying $f$ to singletons, quite distinct from $f(\{a_p\mid p\in P\,\})$.

share|improve this answer

How about saying

In the case that $A=\{a_p\}_{p\in P}$ is a singleton, then $f(A)$ ...

One need not put the responsibility on the notation for indicating your set is a singleton; you can just tell your readers.

Thomas's suggestion of dropping the subscript and writing $\{a\}$ and $f(\{a\})$ is also good.

Since we don't know the context of what you're writing, perhaps neither of these are viable options.

share|improve this answer

Your Answer


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.