Recently I studied something known as characteristic function (Indicator function), after going through it deeply I want know if the set of all characteristic functions on A will be similar to its power set P(A)?
$\endgroup$ 21 Answer
$\begingroup$A characteristic function on $A$ is a function of domain $A$ and range $\subseteq\{0,\,1\}$. Matching such a function $\varphi$ with $\{x\in A|\varphi(x)=1\}$ bijects the characteristic functions on $A$ with the subsets of $A$ (and so does using $\{x\in A|\varphi(x)=0\}$, but that's a bit confusing).
$\endgroup$
