Converting a set to a tuple? Okay, so, let's say I have a set:
$\{0,1,2,3\}$
And I want to convert it to a tuple:
$(0,1,2,3)$
How would I do this? Would it be as simple as:
$f(\{0,1,2,3\}) = (0,1,2,3)$
??
 A: Converting $\{0,1,2,3\}$ to $(0,1,2,3)$ is not well defined since sets are unordered but tuples are. This means $(3,2,1,0)$ would be an equally valid image for the original set.
A way to avoid this problem is to let each position in the tuple designate a particular element and use either a 0 to denote that element is absent from the set and a 1 to denote that it is present in the set.
For example, if your universal set is $\{0, 1, \dots, 5\}$, then $\{0,1,2,3\}$ would map uniquely to $(1,1,1,1,0,0)$ (if we make the appropriate assumption that position zero in the tuple corresponds to the element $0$ from the set, and so forth).
Defining the function in this way has the added advantage that it is a bijection between the power set of your universal set and the collection of all binary tuples of the appropriate length.
A: The conversion depends on a choice of ordering you make; the main difference between the set {$1,2,3,4$} and the 4-ple $(1,2,3,4)$, is that, in the 4-ple, the ordering matters, while in the set , the only thing that matters is whether an element is in the set or not. This means that the set {$1,2,3,4$} equals ${2,1,3,4}$ , but the 4-ple $(1,2,3,4)$ is not equal to , e.g., $(2,1,4,3)$ ; -ples are usually called "ordered n-ples" for this reason, because different orderings designate different n-ples. So, unless you specify a choice of ordering, going from one to the other is ambiguous. Think about this: If {$1,2,3,4$} is mapped into $(1,4,2,3)$, what would, e.g., {$2,3,4,5$} be mapped to?
