Is there an algorithm to find all subsets of a set? I'm trying to find a way to find all subsets of a set.  
Is there an algorithm  to calculate this? 

An algorithm is type of finite procedure operating on finite data as input and generating a finite output. So you can only have an algorithm to find the subsets of $\Sigma$ if $\Sigma$ is finite. (You've been given some hints for that case, but it is important to stress that these hints only work for finite $\Sigma$.)
