I have a function $g()$ that maps a tuple to a set.
$$g(f_1,f_2,…,f_n) = a.$$
-
$a$ is a subset of the natural numbers.
-
The tuple has binoard indicators.
Now, say $n=3,$ the function works as follows:
$$g(0,1,1) = \{2,3\}.$$
I want to write in set notation how this function works, all I can get to is this:
$g(f_1,f_2,…,f_n) = a$
where $a = \{1 \text{ if } f_1 = 1, 2 \text{ if } f_2=1,\dots ,n \text{ if } f_n=1\}.$
So this is how the function works, but obviously there is a better way to write this mathematically, any help? Thx
Best Answer
What you're suggesting is that $k \in g(f_1, \dots, f_n)$ if and only if $f_k = 1$. So you could use set-builder notation to write $$g(f_1, f_2, \dots, f_n) = \{ k \mid f_k = 1 \}$$