This question already has an answer here:
I'm trying to understand why the product of transpositions for a specific permutation is not unique. Intuitively, it somewhat makes sense to me since I can get the answer but I don't actually know why it works.
The example I am particularly confused over is: say I have a permutation which in cycle notation is of the form:
Then I have been given two examples of transpositions that work:
Is it like you treat each transposition as a bijection that belongs to (in this case) S5 (or for any N>5) and so you consider the product of transpositions as a composition of all these bijections - which is why you start from the right and work your way backwards bracket by bracket and you stop once that number doesn't appear anymore? Is this also the case for a product of permutations?