# Shorthand for $0<i<1$ , $0<j<1$, $0<k<1$

Is it good style to write $0<i<1$, $0<j<1$, $0<k<1$ as $0<i,j,k<1$?

The following does not seem so clear:

$0<i,j<1$

as it may be interpreted as: $0<i$ and $j<1$ or $0<i<1$, $0<j<1$

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Yes, that’s fine. – Brian M. Scott Jun 25 '12 at 17:35
In my opinion yes – Belgi Jun 25 '12 at 17:38
I assume there is no order among $i$, $j$ and $k$. – Babak S. Jun 25 '12 at 17:40
Another option is $i,j,k \in ]0,1[$ (or $i,j,k \in (0,1)$) depending on how you prefer to write open intervals. – mrf Jun 25 '12 at 17:59
If there is danger of it being misunderstood, then you can state early on that when you write "$0\lt i,j\lt 1$" etc. you mean that each of $i$ and $j$ lies between $0$ and $1$. – Arturo Magidin Jun 25 '12 at 20:13

It depends on context.

Let $0\le a$, $b\le 0$ and $c = a - b$. Then $0\le c$.

You can use an interval instead: $i,j,k\in (0,1)$.

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It is okay. The comma indicates that there is no necessary relation between $i,j$ and $k$.

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I would definitely interpret $$0 < i,j < 1$$ as $$0 < i < 1 \text{ and } 0 < j < 1. \quad (*)$$ I would not interpret it as $$0 < i \text{ and } j < 1. \quad (**)$$ It is conventional, when writing a single inequality between a variable and a constant, to put the variable on the left, so if I meant (**), I would write $$i > 0,\, j < 1.$$

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I think you meant $j \lt 1$ (or maybe $1 \gt j$ to avoid confusion) in $(\ast\ast)$ and afterwards. – t.b. Jun 25 '12 at 20:19
@t.b.: Fixed. I thought something didn't seem quite right. – Nate Eldredge Jun 25 '12 at 21:44