how to proof that φ:P(N)→2N φ(A)=f where f(n)=1 if and only if n∈A is bijective?
30021
Bijection between set of all binary sequences and power set of $\mathbb N$.
21707
Constructing a Bijective function via an injective and surjective one.
25187
Why $∀x(P(x)→Q)$ is equivalent to $∃xP(x)→Q$
156905
Prove $f_n$ has a uniformly convergent subsequence on $[0,1]$.
75614
Proving that $n|m\implies f_n|f_m$
96894
Prove $f_{n+1}^2+f_n^2=f_{2n+1}$
45710
Finishing a proof: $f$ is injective if and only if it has a left inverse
53101
Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
880
Find all n such that $\phi(n) = n/2$
110662
Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
124333
A bijection between $\mathbb{N}$ and $\mathbb{P}(\mathbb{N})$?
100515
Prove that if $d$ divides $n$ then $φ(d)$ divide $φ(n)$ for $φ$ denotes Euler’s φ-function.
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
52565
Prove that if $d \mid n \in \mathbb{N}$, then $\varphi(d) \mid \varphi(n)$.
46746
How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
96341
Proving $v(s,p)=2^{p-1}(2s-1)$ is a bijection of natural numbers and $f(s)=2s-1$ is a bijection between natural numbers and odd numbers.
82675
What is an example of function $f: \Bbb{N} \to \Bbb{Z}$ that is a bijection?