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

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) $$(a_1,a_2,a_3)$$ ?

• The operation isn't clear. if the original set is unordered we have $\{a_1,a_2,a_3\}=\{a_3,a_1,a_2\}$ so would the image of your operation be $(a_1,a_2,a_3)$ or $(a_3,a_1,a_2)$?
– lulu
Jan 22, 2019 at 18:20
• @lulu Thanks. What I want to formally say is the following: I start my discussion with a set $\mathcal{A}\equiv \{a_1,a_2,a_3\}$. Then I want to tell the reader to fix any ordering of $\mathcal{A}$ and perform some operations with the resulting tuple.
– TEX
Jan 22, 2019 at 18:28
• How can do that formally?
– TEX
Jan 22, 2019 at 18:28
• I think the way you said it is clear. With finite sets there is no problem with choosing. I think it's always worth making it clear that a choice is involved, even if you are indifferent to the choice being made.
– lulu
Jan 22, 2019 at 18:30
• math.stackexchange.com/questions/851667/… Jan 22, 2019 at 19:10

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.