How to express/write a permutation of a Set? How to express a permutation (without repetition) of a Set $A$?
I'd like to create a set $P$ of tuples while equal tuples should only occur once in the set $P$. Tuples are equal when e.g. $\{a, b\} = \{b, a\}$. Tuples of the same values should not be included, e.g. $\{a, a\}$. 
Example: Given $A = \{a, b, c\}$, I would like to receive $P = \{\{a, b\}, \{a, c\}, \{b, c\}\}$. 
How can I write this in an equation?
 A: A concise description of the sets you seek, using set builder notation, are:
$P=\{\{a,b\}:a,b\in A\}$
$P^{\prime}=\{\{a,b\}:a\neq b\textrm{ and }a,b\in A\}$
Edit: In light of comments since posting this, the set you desire appears to be $P^{\prime}$ above, which can also be described as in user3313320's answer.
A: Let $A$ be an $n$-element set.  The set of all $2$-element subsets of $A$ is the set $A^{\{2\}} := \{ B \subseteq A: |B| = 2\} = \{ \{a,b\}: a, b \in A, a \ne b \}$.  The cardinality of this set is ${n \choose 2}$.   But this set does not contain $2$-subsets of the form $\{a,a\}$ which contain repeated elements. 
If you want to repeat elements, the objects you are interested in are called  multisets.  The multisets $\{a_1,a_1,a_2\}$ and $\{a_1,a_2\}$ are distinct (and have cardinalities $3$ and $2$, respectively), although these two multisets are the same set.  What you are looking for then is the set of all multisets of $A$ of cardinality $2$.  
A: $P=\{C|C\subset A \text{ and }|C|=2\}$ should work.
In words, it is the set of all subset of $A$ with two elements.
