Notation for show that a variable is binary?

Question

Are there a "math letter" that represent the set of binary variable $\{0,1\}$? Like, when writing e.g., $a \in \mathbb{R}$, we know $a$ is real.

I only know this notation $a \in \{0,1\}$, but is this the only way to write it?

Thank you in advance

Answer 1

$a \in \{0, 1\}$ means that $a$ is either $0$ or $1$. Similarly with $a \in \mathbb Z_2$.

If you want to designate that $a$ is a binary number with one or more digits, each digit from $\{0, 1\}$, then you might want to simply designate the base in the usual way we do this for a number: $a_2$, though you should make explicit, if you do this, how you are using this subscript.

Alternatively, we can consider a binary number $a$ to be an $n$-tuple, with each component in $\mathbb Z_2=\{0, 1\}$, we can then say $\;a \in \mathbb Z_2^n$.