Notation for a function with the domain $1$ or $0$?

Question

I don't know if "binary function" is the correct name for the following?

I have the functions $f$, $g$, and their domains are only $1$ or $0$.

What is the correct notation for this?

I have the following (? are $1$ or $0$): \begin{align} f:?\rightarrow \mathbb R \tag 1 \end{align}

And for the vector-valued function $g$: \begin{align} g:?\rightarrow \mathbb R^n \tag 2 \end{align} where $g(?)=(g_1(?), \dots, g_n(?))$.

Thanks!

Answer 1

I do not think that the term "binary function" would be appropriate. Indeed, since a binary sequence is a function from $\mathbb{N}$ to $\{0, 1\}$, I would rather see a binary function as a function with range $\{0, 1\}$.

I have no good suggestion for a better name, but you could represent such a function as a pair of reals $(r_0, r_1)$ (where $f(0) = r_0$ and $f(1) = r_1$).

Answer 2

These are similar to two-element tuples, with indexes taken from $\{0,1\}$. The elements are reals or vectors.

Such tuples can be called doubles, couples, pairs or duads. (https://en.wikipedia.org/wiki/Tuple#Names_for_tuples_of_specific_lengths)

Then I would suggest duad functions.