query: Bijections from $A$ to $B$, where $A$ is the set of subsets of $[n]$ that have even size and $B$ is the set of subsets of $[n]$ that have odd size
positive_passages.docid: 21152
positive_passages.text: Exactly half of the elements of $\mathcal{P}(A)$ are odd-sized
negative_passages.docid: 117793
negative_passages.text: Finding a function $\mathbb{N} \to \mathbb{N}$ that is surjective but not injective.
negative_passages.docid: 15909
negative_passages.text: Bijection from $\mathbb R$ to $\mathbb {R^N}$
negative_passages.docid: 146436
negative_passages.text: Cardinality of the set of bijective functions on $\mathbb{N}$?
negative_passages.docid: 82675
negative_passages.text: What is an example of function $f: \Bbb{N} \to \Bbb{Z}$ that is a bijection?
negative_passages.docid: 17268
negative_passages.text: Cycles in permutations of a given size
negative_passages.docid: 67644
negative_passages.text: How does one get the formula for this bijection from $\mathbb{N}\times\mathbb{N}$ onto $\mathbb{N}$?
negative_passages.docid: 63267
negative_passages.text: Under what conditions on the sets $A$ and $B$ will it be true that $A\times B= B\times A$
negative_passages.docid: 76405
negative_passages.text: Let n be an even integer. How many different ways can I choose subsets of the set {1,2...,n}
negative_passages.docid: 72256
negative_passages.text: Prove there exists two sub-sets of indices $I,J\subseteq [2n]$ such that $\sum_{i\in I}a_i=\sum_{j\in J}b_j$
negative_passages.docid: 7938
negative_passages.text: Number of Homomorphisms from $\Bbb{Z}_m$ to $\Bbb{Z}_n$
negative_passages.docid: 2900
negative_passages.text: How many $3$-subsets of $\{1,2,\ldots,10\}$ contain at least one even and one odd integer?
negative_passages.docid: 70278
negative_passages.text: $A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
negative_passages.docid: 147484
negative_passages.text: For a set with N members, what is the number of set partitions in which each subset is either of size 1 or 2?
negative_passages.docid: 117658
negative_passages.text: A set with n elements has 2^n subsets
negative_passages.docid: 110464
negative_passages.text: Let $A=\{1,...,n\}.$ Show that there is a bijection of $P(A)$ with the cartesian product $X^n$ where $X$ is the two element set $X=\{0,1\}$
negative_passages.docid: 124333
negative_passages.text: A bijection between $\mathbb{N}$ and $\mathbb{P}(\mathbb{N})$?