Notation for an interval when you don’t know which bound is greater

Is there a notation in English written mathematics for \textit{the interval of all points lying between two real numbers $a$ and $b$} when you don’t know which of a and b is greater?

Which one is greater is completely irrelevant for what I am writing, and I would like to avoid making the text heavier as much as possible.

Suggestions that have been made so far that rely on external notions:
[\min\{a,b\}, \max\{a,b\}]\qquad \operatorname{Conv}(a,b)

Suggestions for a brand new notation: (a,b]^*\qquad (\{a,b\}]\qquad (a\nearrow b]\qquad /a,b/\qquad \left(\begin{matrix}a\\b\end{matrix}\right]^\star

^\star intervals open at the lower bound and closed at the higher bound, whichever of a and b they are.

Some other options:

  • Assume wlog that a<b
  • Make explicit that the notation [a,b] doesn't imply a<b.


One possibility is \operatorname{Conv}(a,b): the convex hull of a and b. Maybe this should really be \operatorname{Conv}(\{a,b\}), but I think it is forgivable to omit the curly braces - or even to write \operatorname{Conv}\{a,b\}, which keeps it clear that order does not matter.

When a,b \in \mathbb R, this just gives us the closed interval [a,b] or [b,a]; for points a,b \in \mathbb R^n, this gives us the line segment from a to b.

It generalizes to \operatorname{Conv}\{a,b,c\} which is the smallest closed interval containing all three of a,b,c \in \mathbb R, and so on.

Source : Link , Question Author : Arnaud Mortier , Answer Author : Misha Lavrov

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