Notation of a set which contains all numbers of an interval

Question

How to denote that a set $S$ contains all the numbers of a discrete interval interval $I$?

For example: be $I = [0, 3]$, thus $S = \{ 0, 1, 2, 3 \}$.

The best I came up with is $S = \{ \min(I), ..., \max(I) \}$, but I think $\min/\max$ are pretty non-standard for this.

Answer 1

The usual notation for $\{a,a+1,\dots, b\}$ is $[[a,b]]$, although it's not really all that common and I almost always have to explain what it is in real life.

In your particular case you may want to use $S=I\cap \mathbb Z$

Answer 2

How about $$S = I \cap \mathbb{Z}$$ ?

Answer 3

As other people said, in your example you could write

$$S=\left(\bigcup_{j\in J} I_j\right) \cap \Bbb{Z}$$.

You can also explicitly say something like:

$$S=\{x\in I_i:\text{insert rule(s) for x here}\}$$

In your example, you'd write: $$S=\{x\in I_j:x\in\Bbb{Z}\ \text{and} \ j\in J\}$$