In a mathematical context: Let's say x is contained in an interval I. How can I express this as a noun equivalent (but correct) to the "containedness"? I found things like "inherence", "immanence", but they don't seem to fit perfectly

  • I think that this is too domain-specific to be answered on a general English Language forum. It should probably be migrated to math.stackexchange.com Jul 26 '16 at 11:26
  • 'X is a subset of Y' -> containment'/'subset relation', 'X is a member of Y' -> 'membership'
    – Mitch
    Jul 26 '16 at 12:48

Speaking in mathematical terms, inclusion sounds like a good candidate.

In your example, you could be writing a "proof of inclusion of x in I"

Relevant Wikipedia page:


  • that fits very well, how could I not think of this... Thanks! Jul 26 '16 at 11:27
  • The same page also mentions "containment" but might be specific to set theory. Jul 26 '16 at 11:29

I am a set theorist and have so far found no satisfactory way of expressing this: I don't believe there is any adjective to describe "being a subset of" that couldn't also mean "being an element of." "Inclusion of x in I" doesn't cut it, for example; that could mean that x is an element of I. Same with "containment" and the verb-phrase "is contained in." Unless it's totally clear from context, I'd use "is an element of" or "is a subset of" always.

  • thanks, that is an interesting comment! I think that in my case (of I being an interval on the real line), "inclusion" is the right word to use, but I agree that there is general lack of a suitable noun Jul 26 '16 at 12:04
  • Yes, if x is a point and I an interval, then "inclusion" is absolutely fine. These problems occur a lot more often in set theory, where the types of objects are sometimes less clear. Jul 26 '16 at 15:43
  • @ChrisLeSueur Lack of a noun is a really annoying problem when you deal with abstract concepts. This is one of the reasons I do not agree with the prescriptivist view of language. On the other hand, prescriptivism allows one person to "discover" something and get to name it, as opposed to many, many people agreeing to use a word. This is great in most cases but low-usage-count (see? no proper word!) situations (like a lot of mathematics, I mean, how many people would feel an acute need for a word you described? But the word is missing...) tend to leave you with weird constructs or un-words. Jul 26 '16 at 16:53

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