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In an n-dimensional Euclidean space, what is the correct term for an n-dimensional object inside another one? See this image as a three-dimensional example. Is saying "The smaller cube is inside of the bigger one" correct? Does that apply to 3+ dimensional Euclidean spaces? Thanks in advance.

Edit: Can "Contain" be used for line segments in 1-dimensional spaces?

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  • $\begingroup$ Inscribed ????? $\endgroup$ – Rene Schipperus Sep 7 '16 at 14:07
  • $\begingroup$ @ReneSchipperus I don't think so, sorry. $\endgroup$ – user307244 Sep 7 '16 at 14:08
  • $\begingroup$ Inscribed would be appropriate if the boundary of the 'interior' object touched the exterior object's boundary in a maximal sense. (An inscribed triangle, for instance, is one which lies inside a circle and touched it at three points.) Perhaps one could say that the bigger cube contains the smaller cube? (The image used is a bit ambiguous, since without further information one can't really tell if the smaller cube is inside, behind, or in front of the larger cube.) $\endgroup$ – Semiclassical Sep 7 '16 at 14:20
  • $\begingroup$ I think everybody would understand the word "inside". Technically, since regions are often though of as subsets of $\mathbb R^n$, you could denote this as $A \subseteq B$ and say in words that $A$ lies entirely inside $B$. $\endgroup$ – Rahul Sep 7 '16 at 14:30
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    $\begingroup$ Object A is "suspended inside" object B. $\endgroup$ – Mick Sep 7 '16 at 15:20
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Answers from the comments:

  • Inscribed (to be applied in the appropriate situation, where the inner set's boundary touches the outer set's boundary in a maximal sense, as a triangle inscribed in a disk)
  • Contain (consider sets with interior and write $\subseteq$)
  • Inside (perhaps not too informal)
  • Suspended inside
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