I am wondering what notation I should use when writing that some variable is an integer within some range. What is the most common way to do this? Here are some ideas I have but I'm not sure what the usual convention is.
For example, an integer on the interval [0,29], would I denote it as:
$$
x\in [3,29]\cap \mathbb{Z}
$$
or something of the sort like
$$
x \in \{ k \mid k \in \mathbb{Z} \wedge k \geq3 \wedge k\leq29\}
$$
or some combination of both maybe? I know different standards exist but I'm sure there's a "most common one" which I could use, the first that I wrote is the one I've been using so far in texts for personal re-reading. Is it more useful to write it in words when writing something for others to read?
"Let x be an integer less than 30, greater than 2…" or something similar.
Bonus question:
Does this change when talking about strictly natural numbers on a range, how about non-negative integers? i.e x is in a range of [1, n] or [0, z] (where n is some natural number and z some integer), obviously you can change the set in the example but hey, maybe there's a different convention for those. So something like:
"Let x be a natural number less than 30"
This is a little bit of a messy text but hopefully the question is clear
Best Answer
At least in Belgium, high schoolers get taught that $n \in [a, b]$ is the standard notation for a given range of real numbers, so I wouldn't use it straight away. As others have pointed out though, introducing it beforehand is probably the best way to go from a practical standpoint. In my personal opinion, "Let $x \in \mathbb{N} \cap [a, b]$" is the least ambiguous but to people who grew up with $[a, b]$ it'll probably come over as convoluted.