Definition of the ordered triple (a, b, c) according to Kuratowski's Set Theory. Can someone give Kuratowski's definition of the ordered triple $(a,b,c)$ assuming $A \times B \times C$ is rewritten as $(A \times B) \times C$, please? I noticed there is already an answered question for the ordered $n$-tuple, but (as I'm very new to Maths) I didn't understand it, and I only need the definition for the ordered triple. 

Ordered triples are defined recursivley, so that 
$(x,y)=\{\{x\},\{x,y\}\}$ and $(x,y,z)=((x,y),z)$. Observe that $((x,y),z)$ only has two elements, $(x,y)$  and $z$, so we can just apply the definition. To make our lives easier, let $q=(x,y)=\{\{x\},\{x,y\}\}$. Then the substitution is simple: 
$$\begin{align}\label{eqn:einstein} (x,y,z) &= ((x,y),z) \\
&=(q,z) \\
&= \big\{\{q\},\{q,z\}\big\} \\
&=   \big\{\{\{\{x\},\{x,y\}\}\},\{\{\{x\},\{x,y\}\},z\}\big\} \\
\end{align}$$
Likewise, $(x,y,z,w)=((x,y,z),w)$, so letting $q=(x,y,z)$, we can write $(x,y,z,w)=(q,w)= \big\{\{q\},\{q,w\}\big\}$, which we can expand as shown above. 
Substitutions are your friend.  
