How do I format the indices for an indexed equation? [closed]

I have a piecewise cubic function where I define the segments as follows:

\begin{align} \label{eq:segment}
s_i(x) &= a_i(x-x_i)^3 + b_i(x-x_i)^2 + c_i(x-x_i) + d_i &\text{for $i = 1, 2, \ldots, n-1$}.
\end{align}


Is there a standard way to specify the valid values of i? Here are things I've thought about and what I don't like about them:

• for $i = 1, 2, \ldots, n-1$ - takes up a lot of space (not ideal for longer equations).
• for $1 \le i \le n-1$ - makes i look continuous.
• for $i \in [1, n-1]$ - makes i look continuous.
• for $i \in \mathbb{N}(1, n-1)$ - I'm not sure if this is valid notation for a range of natural numbers, or even if a compact notation like this exists.
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I'd go with one of the first two options. However, I don't think that this question is on-topic. – Caramdir Jul 27 '11 at 4:22
@Caramdir Do you mean the first of the four options? Would this question be more appropriate on Math.SE? If so, what's the best way to migrate it? – Brandon Jul 27 '11 at 4:30
It would take a moderator to move it to Math.SE. For what it's worth, for a compact notation I would go with option 2. The use of i and n certainly suggests that both are integers so I disagree with your conclusion. If you really feel that this is ambiguous (maybe because of earlier stuff) you could put a phrase before the equation "in which (i) is an integer" or even "in which (i) is an integer strictly between (0) and (n)". – Andrew Stacey Jul 27 '11 at 9:48
Those brackets should have been $$ and $$s. – Andrew Stacey Jul 27 '11 at 9:48
@Brandon: I meant that I'd use version one or version two. – Caramdir Jul 27 '11 at 16:02

closed as off topic by egreg, Andrew Stacey, Caramdir, Brandon, Lev BishopAug 3 '11 at 5:02

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There is also set notation:

\left\{ 1\le i \le n-1 \middle\vert i \in \mathbb{N} \right\}

It looks more 'mathematical' but does not save a lot of space.

P.S. It seems that the question has little to do with TeX.

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 The above notation, referred to as set builder notation is defined according to ISO 80000-2:2009, Mathematical signs and symbols to be used in the natural sciences and technology. It superseded the historical ISO 31-11. – Werner Jul 27 '11 at 22:34

Of the options you listed, 2 is best. Although it looks continuous, the context makes it clear it's discrete. The first version is sloppy math (but done a lot); it looks like $i$ is equal to a finite sequence. Options 3 and 4 aren't standard.

I just realized that options 3 and 4 indicate that you probably aren't using the amsmath package. Put \usepackage{amsmath} in the preamble and try

for $i \in \{1,2, \ldots, n-1 \}$

This is the most precise way to define your cubic function.

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