Notation for the operator that transforms sets (unordered) into tuples (ordered)?

Question

Take a set $\mathcal{A}\equiv \{a_1,a_2,a_3\}$ of real numbers.

Is there any specific notation in math for the "operator" that transforms $\mathcal{A}$ into the 3-tuple (ordered) $$ (a_1,a_2,a_3) $$ ?

Answer 1

I'm assuming for this function you want to find, you'd sometimes want a sequence with repeated elements. If this is the case, then the answer to you question is no.

Example:

If there was such a function that did this, say, $f$, then since $\{5\} = \{5,5\}$, you'll have

$f(\{5\}) = (5)$

and

$f(\{5,5\}) = (5,5)$

which doesn't make $f$ a function.