I am trying to prove that the cardinality of P(N) (the set of all finite subsets in N) is equal to the cardinality of N.
41661
Show that the set of all finite subsets of $\mathbb{N}$ is countable.
124060
Are these subsets of the powerset P(N) countable?
16553
Cardinality of the set of all total orders on $\Bbb{N}$
96903
How to show via inductive proof (and without the use of the binomial theorem) that $ {n\choose k} \in \mathbb{N} $?
125683
Power set of a finite set is finite proof, no cardinality of power set
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
109968
Let $X= \{ A \subset \mathbb{N} : \mathbb{N} \backslash A \text{ is finite}\}$. What is the cardinality of $X$? Prove it.
152342
$x_1+x_2+\cdots+x_n\leq M$: Cardinality of Solution Set is $C(M+n, n)$
128437
How to prove that a finite set is countable
147013
Subset of a finite set is finite
73850
Cardinality of set of functions
66301
The cardinality of the set of countably infinite subsets of an infinite set
144735
Possible cardinality of power sets
89712
For every set $A$, the empty set is a subset of $A$. The empty set is a set. Therefore, the empty set has a cardinality $\geq 1\ldots$
45216
Cardinality of $[0,1]$
70282
Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
65768
What is the cardinality of the set of the empty set?