Writing a Permutation as a product of Disjoint Cycles How do i write a permutation as a product of disjoint cycles ?

I know that in order to determine a cycle we need to start with the smallest element and move on till the mapping points to itself.Then start with the next non repeating smallest element..But how to write this as a product of disjoint cycles?
 A: First, we note that writing it as a product of disjoint cycles means that each number appears only once throughout all of the cycles.
We see that $1\mapsto 5$, $5\mapsto 3$, $3\mapsto 2$, $2\mapsto 1$. So, we can express this in cycle notation as 
$$(1532).$$
Now, we see what is left over... well, that is just $4$, which is fixed by the permutation in question. So, the permutation can be written as
$$(1532)(4),\mbox{ or equivalently, just } (1532).$$
A: $4$ is the only one invariant, while the others mingle among them, thus there are only two cycles
$$(1\,5\,3\,2)$$
It's customary not to write any singleton.
A: You start with the first number than you go to the number with is under this number and so on until you get back to the start number...... In your case you start with 1 then go to 5 then to 3 to 2 and are back at one,.... So the first cycle is (1;5;2;3)
Then you look at the numbers which aren't in the first cycle e.g. 4 and do the same again.... ( you can, but you do not have to mention cycles with length 1 if it is known in which Sn the permutation is or it is otherwise clear how long the permutation is.)
