How do you denote the opposite of a range of numbers? What I want to do, is find the conventional standard to denote a range of numbers not included in a set, which is itself part of an infinate set.

For e.g:

A range of numbers, from say, -∞ to 0, and from 1,000,000 to ∞ i.e every number except, 1 through 1,000,000.
The most common notation would be $\mathbb Z\setminus\{1,2,3\}$ or $\mathbb Z-\{1,2,3\}$, where $\mathbb Z$ is the set of all integers. Notably, this would not include $\pm\infty$, since $\infty$ is not a number. Since this may get cumbersome if you wanted to leave out a lot of numbers-- say all the integers from one to one million--then you could say $\mathbb Z\setminus\{1,2,...,1{,}000{,}000\}$.

Sometimes sets of numbers are denoted $[a,b]$ for real numbers $a$ and $b$. This means the set of all numbers between $a$ and $b$ inclusive including decimals. Saying $\mathbb Z\setminus [1,10^6]$ still means the same thing, though because it indicates that we are removing all the numbers between $1$ and $10^6$ from $\mathbb Z$. If some of them weren't in $\mathbb Z$ to begin with, that is fine.
Another way is to reverse the
direction of the brackets
and exchange
open and closed.

For example,
the complement of
"(0, 1]"
would be
"]0, 1(".