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If I have an expression like $$ \mu^i(x,t) = 0 \qquad, \qquad \qquad i=1,\dots, K $$

I want a more compact way of specifying that the index $i$ takes integer values from $1$ to $K$. I'm looking for something like $i\in I_1^K$, or $i\in \mathbb{Z}_1^K$, etc. Is there a standard notation for this that I have missed? Something like $i\in [1,K]$ does not work as it does not make clear that $i$ is an integer.

kipf
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J Peterson
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  • I'm not aware of any standard notation for this aside from the "less compact" one you give above – Jonathan Pal Apr 07 '23 at 18:28
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    Some people use $[K]$ as notation for the set ${1,\dots,K}$. (but also sometimes ${0,\dots,K}$ or ${0,\dots,K-1}$) But frame challenge: the goal of mathematical writing is clarity, not compactness—and $i=1,\dots,K$ is extremely clear as well as quite compact. – Greg Martin Apr 07 '23 at 19:45
  • @GregMartin yes that is true and in my example there would be no need for more compact, perhaps less clear, notation. But I often have work with lots of indices ranging over different numbers and specifying each as $i=1,\dots, K$ quickly gets cumbersome and equations are cluttered with index ranges. Just using $i\in[K]$, $\alpha\in[N]$, etc. as you mentioned would be nice. – J Peterson Apr 07 '23 at 20:23
  • if @GregMartin 's suggestion suits you, define $[k]$ and use it. +1 for the frame challenge in his comment. – Ethan Bolker Dec 12 '23 at 20:48

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