The well-known notation for continuous intervals is $[a,b]$. But what's the case for discrete intervals? Actually they are sets of finite elements $\left\{a, a+1, ..., b-1, b\right\}$ or infinite elements $\left\{0, 1, 2, ...\right\}$.

Is there any special notation or common practice for discrete intervals?

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    $\begingroup$ Isn't $[a,b] \cap \mathbb Z$ enough? $\endgroup$ – Santiago Aug 11 '16 at 19:21
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    $\begingroup$ See math.stackexchange.com/questions/1188685/… for the earlier version that I found by now. I cannot vote as dupe, and will vtc the other one. $\endgroup$ – quid Aug 11 '16 at 19:30
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    $\begingroup$ I have seen $\mathbf{Z}_{a,b}$, but that might be very uncommon. $\endgroup$ – user305860 Aug 11 '16 at 19:37

A notation that is sometimes used is double-brackets, so $[[a,b]]$. (But it should still be explained what is meant.)

If one uses only the discrete version it is not uncommon to just use the usual notation $[a,b]$ for the discrete version, and to say so clearly somewhere.

Let me add that on an earlier question regarding this subject the notations $a..b$ and $[a..b]$ were also mentioned.

  • $\begingroup$ I believe to have answered this already but could not find it. $\endgroup$ – quid Aug 11 '16 at 19:25

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