# What does the semicolon (";") mean in "$a\in(2;3)$"?

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

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?

• Without further context, I’d suggest that this is supposed to mean the open interval corresponding to $2<a<3$. Oct 17, 2019 at 21:34
• 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. Oct 18, 2019 at 1:28

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