query: Defining bijective function $f:\mathbb{N}\times\mathbb N\to\mathbb N$
positive_passages.docid: 6161
positive_passages.text: The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
negative_passages.docid: 109710
negative_passages.text: Bijection between $\mathbb N \times \mathbb N$ and $\mathbb N$
negative_passages.docid: 74453
negative_passages.text: Injective and Surjective Functions
negative_passages.docid: 154754
negative_passages.text: Is $O_n$ isomorphic to $SO_n \times \{\pm I\}$?
negative_passages.docid: 40868
negative_passages.text: Composition of two functions - Bijection
negative_passages.docid: 114118
negative_passages.text: Define the image of the function $f :\Bbb Z \times \Bbb N →\Bbb R$ given by $f(a, b) = \frac{a−4}{7b}$?
negative_passages.docid: 64866
negative_passages.text: Proving a Composition of Functions is Bijective
negative_passages.docid: 128652
negative_passages.text: Subgroups of $\mathbb Z \times(\mathbb Z/n\mathbb Z)$
negative_passages.docid: 114916
negative_passages.text: $\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
negative_passages.docid: 15909
negative_passages.text: Bijection from $\mathbb R$ to $\mathbb {R^N}$
negative_passages.docid: 141225
negative_passages.text: Number of all bijective functions from A to A.
negative_passages.docid: 12825
negative_passages.text: Bijection between $2^{\mathbb R}$ and $\mathbb{ R ^ R}$
negative_passages.docid: 144445
negative_passages.text: Functions $f:\mathbb{N}\rightarrow \mathbb{Z}$ such that $\left(m-n\right) \mid \left(f(m)-f(n)\right)$
negative_passages.docid: 94059
negative_passages.text: Extending a Homotopy from $X \times [0,1]$ to $X \times \mathbb{R}$
negative_passages.docid: 55393
negative_passages.text: Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
negative_passages.docid: 23464
negative_passages.text: How to find a explicit bijection for some $f:A\times B \rightarrow B \times A$
negative_passages.docid: 50649
negative_passages.text: On the existence of a continuous bijection $f\colon [0,1]\to [0,1]\times [0,1]$