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.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let's say I have a set $S$ and I want all subsets that have two elements. Is there a special name for that?

To put it another way, I want to know if there is a name of the subset of a $S$'s power set that have $n$ elements.

share|cite|improve this question
$k\phantom{}$-subsets? – J. M. Nov 2 '11 at 16:41
The number is determined by a binomial coefficient, C(n,r) giving the number of subsets of order r of a set with n elements. Outside of saying the number of doubletons for your example with r=2, I don't know of any special name attached. Of course if the cardinality of S is infinite, then everything I've said above is not very useful. – Chris Leary Nov 2 '11 at 16:41
@Joe - J.M. has it, I think. It's certainly a good name, even if by some chance it's not standard. – Chris Leary Nov 2 '11 at 16:43
I've seen it notated $\binom{S}{2}$, but I don't think that's a standard notation. – Henning Makholm Nov 2 '11 at 16:44
up vote 3 down vote accepted

The standard name is something like the (set of) $n$-subsets. Less common is $n$-combinations.

share|cite|improve this answer

The number of subsets of size $k$ in a set of size $n$ is often denoted $\dbinom nk$, called "$n$ choose $k$".

The set of all subsets of size $k$ in a set $S$ of size $n$ is sometimes denoted $\dbinom Sk$. For example, $\dbinom{\{a,b,c,d\}}{2} = \{\ \{a,b\}, \{a,c\}, \{a,d\}, \{b,c\}, \{b,d\}, \{c,d\} \ \}$.

I sometimes just call them "size-$k$ subsets of $S$".

share|cite|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.