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I'm working on a linear program and I have the following constraint:

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I'm wondering what does the ";" mean? At first I thought it meant the variable $a$ can only be $2$ or $3$, but that's what $(2, 3)$ is for, right?

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    $\begingroup$ Without further context, I’d suggest that this is supposed to mean the open interval corresponding to $2<a<3$. $\endgroup$
    – Benjamin
    Oct 17, 2019 at 21:34
  • $\begingroup$ Well, either they mean $\{2,3\}$ and use the $;$ to distinguish it from the interval $(2,3) =\{x|2<x < 3\}$.... or they mean the interval $\{x|2<x<3\}$ and the use the $;$ to distinguish it from the ordered pair $(2,3) \in \mathbb Z\times \mathbb Z$ or the set $(2,3)=\{2,3\}$. ... Unfortunately there is a lot of ambiguity in notation and this isn't clear. But inclined to think it means $\{x|2<x<3\}$. BTW I'm surprised you said "that's what $(2,3)$ is for"; I'm inclined to believe $(2,3)$ in nearly universally meant to mean the interval and that only $2$ or $3$ is what $\{2,3\}$ is for. $\endgroup$
    – fleablood
    Oct 18, 2019 at 1:28

1 Answer 1

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The open interval of numbers between $a$ and $b$ is often denoted as $(a,b)$. However, in some countries where comma $(,)$ is used as decimal points, a semicolon $(;)$ may be used in place of a comma as a separator to avoid ambiguity: for example, the open interval from $0$ to $1$ would be written as $(0;1)$.

In the example above $a\in(2;3)$ means that $a$ is an element in the open interval from $2$ to $3$.

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    $\begingroup$ Also, sometimes a double dot is used. $a\in(2\,.. 3)$ $\endgroup$ Oct 18, 2019 at 1:29

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