Is there a standard shorthand for the set $\{0, 1, \dots,k-1,k+1,\dots,n-1,n\}$?

Question

The question title pretty much says it all.

In derivations where there's some fancy footwork being done with indices, I find expressions like

$$\sum_{i \neq k} x_i$$

a bit too vague. On the other hand, this is explicit enough, but just too unwieldy and awkward-looking:

$$\sum_{i \in \{0, 1, \dots,k-1,k+1,\dots,n-1,n\}} x_i$$

(Of course, I can invent my own notation, but I consider this the "the nuclear option.")

Maybe ${x \in \mathbb{Z}^{nonneg} | x \le n \wedge x \ne k}$? Or is that not short? — 2012ssohn, Dec 25 '13 at 03:33

score 4 · Accepted Answer · answered Dec 25 '13 at 03:12

4

I've seen $\{0,\dots,\hat{k},\dots,n\}$, but that's not much shorter.

Alternatively, $[n]$ is often shorthand for $\{1,\dots, n\}$, so you could use $[n]\setminus\{k\}$.

answered Dec 25 '13 at 03:12

Alex Kruckman

1 Answers1