In ordered structures, the book says that
A^1 != A
In the example, they say :
Let A = {a,b,c}
A^1 = { (a) , (b), (c) }
How does the parentheses make them different ?
Firstly, saying $\displaystyle A^1 != A$ is not a good practice on a math website. We don't do C++ here, it's $\displaystyle A^1\ne A$. And, although I have actually not seen this notation before my gut tells me that it means $\displaystyle A^1=\left\{\{a\}:a\in A\right\}$ which clearly, set theoretically that is, is not equal to $\displaystyle A$.
It's no problem. I have no idea what your book means. I would interpret it like this. $\displaystyle A^1$ is the set of all singletons in $\displaystyle \wp\left(A\right)$. In other words, take each element of $\displaystyle A$ put it in it's own set and then put it back. And as sets we have that $\displaystyle a\ne\{a\}$.