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I often find myself using the set $\{1,2,..,k\}$, sometimes on multiple occasions in a sentence. I've been told that $[k]$ is a short notation for this, but have never seen that in use. Could someone refer me to a textbook-like source that uses this notation so that I may cite it.

pjs36
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Y2K
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  • I think Norman Biggs uses it in Discrete Mathematics, but I'm not sure. There's always Wikipedia (third paragraph in the linked section). Related question. – Git Gud Oct 02 '15 at 11:05
  • Some times it is $\overline{1..k}$ – Nikita Evseev Oct 02 '15 at 11:06
  • Personally, I like to use $[|1,n|]$ – Tryss Oct 02 '15 at 11:18
  • I usually use either $\bar k={0,1,...,k}$ and $\bar k^*={1,...,k}$ or $[![1,k]!]$. – Surb Oct 02 '15 at 11:23
  • See also http://math.stackexchange.com/questions/521437/standard-notation-for-the-set-of-integers-0-1-n-1 and http://math.stackexchange.com/questions/287251/about-math-notation-the-set-of-the-nth-natural-numbers. – lhf Oct 02 '15 at 11:29
  • Briggs write two brackets to denote different types of equivalence relations, but I did not find the usage $[k]={1,2,\ldots,k}$ in his Discrete Mathematics. I like the $[|1,k|]$ and $[![1,k]!]$ options. They are suggestive and flexible. But I would not want to adopt anything that is not already established. At least the $[k]$ notation is on Wikipedia, although for a reference I would only use a text in print. – Y2K Oct 02 '15 at 12:32

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A very famous textbook using the notation $[n]=\{1,2,\dots,n\}$ is Enumerative Combinatorics (Volume 1) by Richard Stanley. It's in the list of notation at the beginning of the book, and is first used in Example 1.1.16.

Hans Lundmark
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