query: Is there a bijection $\big\{x:\mathbb{N}\to\{0,1\}:\{i\in\mathbb{N}:x(i)=1\}\text{ is finite}\big\}\to\big\{x:\mathbb{N}\to\{0,1\}\big\}$?
positive_passages.docid: 155168
positive_passages.text: Is the collection of finite subsets of $\mathbb{Z}$ countable?
negative_passages.docid: 21114
negative_passages.text: $S=\{(n,{1\over n}):n\in\mathbb{N}\}$ is closed in $X$?
negative_passages.docid: 64866
negative_passages.text: Proving a Composition of Functions is Bijective
negative_passages.docid: 89167
negative_passages.text: Cardinality of equivalence relations in $\mathbb{N}$
negative_passages.docid: 20303
negative_passages.text: A function $f\colon E\to F$ between finite sets is injective iff it is surjective iff it is bijective
negative_passages.docid: 10458
negative_passages.text: How to define a bijection between $(0,1)$ and $(0,1]$?
negative_passages.docid: 157268
negative_passages.text: Proving a bijection with absolute value
negative_passages.docid: 44717
negative_passages.text: Does there exist a bijective $f:\mathbb{N} \to \mathbb{N}$ such that $\sum f(n)/n^2$ converges?
negative_passages.docid: 127488
negative_passages.text: If $L:\mathbb{R}^n \rightarrow \mathbb{R}^m$ and $m<n$ linear trans. What does this tell about injectivity and surjectivity?
negative_passages.docid: 56233
negative_passages.text: Is the set of all strings with countably infinite length bijective to $[0,1]$?
negative_passages.docid: 44689
negative_passages.text: Explicit bijection between $[0,1)$ and $(0,1)$
negative_passages.docid: 141114
negative_passages.text: Question about a bijection between $\mathbb R$ and $\mathbb R \cup \{\infty\}$
negative_passages.docid: 67451
negative_passages.text: Building a bijection from a finite union of countable sets to $\mathbb{N}$
negative_passages.docid: 46971
negative_passages.text: Number of surjections from $\{1,...,m\}$ to $\{1,...,n\}$
negative_passages.docid: 130381
negative_passages.text: bijection from $(a,b)$ to $\Bbb R$
negative_passages.docid: 53168
negative_passages.text: Surjective, Injective, Bijective Functions from $\mathbb Z$ to itself
negative_passages.docid: 59459
negative_passages.text: Binary sequences and ${2}^{\mathbb{N}}$ have the same cardinality