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
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In my opinion yes – Belgi Jun 25 '12 at 17:38
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I assume there is no order among $i$, $j$ and $k$. – Mikasa Jun 25 '12 at 17:40
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3Another 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
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1If 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
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Don't be afraid of words in mathematical writing. Example: "$i$, $j$, and $k$ lie in the open interval $(0, 1)$." – Sammy Black Nov 19 '14 at 05:53
3 Answers
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It is okay. The comma indicates that there is no necessary relation between $i,j$ and $k$.
Asaf Karagila
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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 $$i > 0,\, j < 1.$$
Nate Eldredge
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3I 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
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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: $i,j,k\in (0,1)$.
Minimus Heximus
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