Originally Posted by
Plato First, I must say that I do not think that you are asking the question that you mean to ask.
Because, I see only one element of the set of triples, 3-tuples.
Now, I am of course aware that a set of ordered pairs is defined as sets of sets: the pair $\displaystyle
\left( {a,b} \right) = \left\{ {\left\{ a \right\},\left\{ {a,b} \right\}} \right\}$
And we define the triple $\displaystyle \left( {a,b,c} \right) = \left( {\left( {a,b} \right),c} \right)$.
Therefore, have you asked the question you meant to ask?