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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

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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 $$g(f_1, f_2, \dots, f_n) = \{ k \mid f_k = 1 \}$$

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  • $\begingroup$ Oh of course, thank you $\endgroup$ – user11015000 Sep 20 '20 at 13:46
  • $\begingroup$ @user11015000 Since you seem satisfied by the answer, why don't you accept it? $\endgroup$ – J.-E. Pin Sep 22 '20 at 10:07

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