I wonder if the set of all characteristic function on a set A is similar to its power set P(A)
73221
How can I form a bijection between $\mathcal P(A)$ and $2^A$.
114811
Characteristic subgroups and automorphisms
149364
Characteristic polynomial of an inverse
88598
Property of $\{0^n, 1^n, \ldots\}$
9082
Do sets, whose power sets have the same cardinality, have the same cardinality?
146312
Is the set of roots with respect to their values and multiplicies unique for each $g(x)$ in $a_n x^n + g(x)$?
23125
Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
138069
Proof that $\bigcap_{a\in A} \bigg(\, \bigcup_{b\in B} F_{a,b} \, \bigg) = \bigcup_{f\in ^AB} \bigg(\, \bigcap_{a \in A} F_{a,f(a)}\,\bigg) $
142267
If two sets have the same cardinality, then so do their power sets. Converse can't be answered?
18282
Finding the minimal polynomial, the eigenvalues, and the characteristic polynomial of $T(A)=A+A^t$
79734
Is every sub-lattice of $\mathcal P(X)$ isomorphic to a sub-lattice of $\mathcal P(X')$ containing singleton sets?
25187
Why $∀x(P(x)→Q)$ is equivalent to $∃xP(x)→Q$
128305
$PGL(n, F)=PSL(n, F)$
147659
Counterexample to "if $f:A\to A$ induces the identity $\hat f:\operatorname{Spec}(A)\to\operatorname{Spec}(A)$, then $f=\operatorname{id}_A$"
80397
Show that this set of polynomials is ideal in F[x]
41052
The set of real numbers and power set of the natural numbers
124060
Are these subsets of the powerset P(N) countable?