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 $a<b$.
Best Answer
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.