Permutation is Product of Transpositions

Theorem
Let $S_n$ denote the symmetric group on $n$ letters.

Every element of $S_n$ can be expressed as a product of transpositions.

Proof
Let $\pi \in S_n$.

From Existence and Uniqueness of Cycle Decomposition, $\pi$ can be uniquely expressed as a cycle decomposition, up to the order of factors.

From K-Cycle can be Factored into Transpositions, each one of the cyclic permutations that compose this cycle decomposition can be expressed as a product of transpositions.

The result follows.