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This may be a silly question, but it has been a long time since I have used set notation to any real extent. How would I write that $i$ is an integer ranging from $1$ to $N$?

My (possibly faulty) recollection is that this is expressed as $i \in \{ \mathbb{Z}: [1,N]\}$. Is this correct?

codeAndStuff
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  • The expression that you've written is meaningless; using our traditional translation of symbols to words, it would come out as something like "$i$ is an element of the set of all $\mathbb{Z}$ such that $[1,N]$". If you want to use set-builder notation, you could do basically as @abiessu suggests, with set braces around it. – Nick Peterson Oct 28 '13 at 18:39
  • @NicholasR.Peterson Alright, thanks. – codeAndStuff Oct 28 '13 at 18:43

3 Answers3

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Notationally, to write $i$ is an integer within a given interval, you could write several different things:

$$i\in\Bbb Z:i\in[1,N]\tag 1$$

$$i\in\Bbb Z:1\le i\le N\tag 2$$

$$i\in\Bbb Z\cap[1,N]\tag 3$$

where each is read as follows:

$(1)$ "$i$ is an integer such that $i$ is within the interval $1,N$"

$(2)$ "$i$ is an integer such that $1$ is less than or equal to $i$ is less than or equal to $N$"

$(3)$ "$i$ is an element of the set intersection of the integers with the interval $1,N$"

Each would be considered a valid representation, and each may be considered more appropriate for given circumstances or writing styles than the others.

As mentioned elsewhere, it is also common to write $i=1,2,\dots,N$ especially when $i$ is an indexing element.

abiessu
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  • $i$ is in fact an indexing element in my particular case, but thanks for addressing the more general question. So is it incorrect to write it as in my most recent edit? This seems to be another way to write your case $(1)$.. – codeAndStuff Oct 28 '13 at 18:36
  • I particularly like your third way of writing it though. – codeAndStuff Oct 28 '13 at 18:37
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It is very common in mathematics to write simply $i=1,\ldots,n$.

It is almost an universal truth that $i,j,k$ are natural numbers when we write like above.

Sigur
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  • Yeah, I see that notation all the time, you properly answered my question as first stated. See my edit, this is sort of a silly example but I am trying to remind myself of some the notation generally used in mathematics writing. It's been awhile since I have had to do any formal writing. – codeAndStuff Oct 28 '13 at 18:34
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    So if you want to follow what is done in formal math texts and what is more common, write as I suggested. Please, avoid new and complicated notations. Sometime less is more. – Sigur Oct 28 '13 at 18:37
  • @Sigur Really? A simple typographic change makes them from $i$ to $\boldsymbol{i}$ an so on. Funny, isn't it? After all $i$ is something very special in certain contexts. – Michael Hoppe Oct 28 '13 at 18:43
  • After years reading math we feel free to write simply as I wrote. Since we shouldn't prove everything when we write math (otherwise we would have to start from zero) we should be clear and simple. – Sigur Oct 28 '13 at 18:48
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    I was thrown off by this wiki post on interval math notation. They use two dots which I have never seen, and I'm not sure there is a standard $\LaTeX$ notation for (using two periods spaces them out too much: $i=1,..,n$). – Steven C. Howell Oct 12 '15 at 12:50
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I can't find a reference but I think I have seen this kind of notation: $$i\in \overline{1,N}.$$ At least, it doesn't seem to conflict with any other notation.

Bence Mélykúti
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