Notation for integer between two values
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?
$\endgroup$ 23 Answers
$\begingroup$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.
$\endgroup$ 2 $\begingroup$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.
$\endgroup$ 5 $\begingroup$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.
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