query: Find if set $I$ of all injective functions $\mathbb{N} \rightarrow \mathbb{N}$ is equinumerous to $\mathbb{R}$
positive_passages.docid: 146436
positive_passages.text: Cardinality of the set of bijective functions on $\mathbb{N}$?
negative_passages.docid: 145722
negative_passages.text: Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
negative_passages.docid: 46863
negative_passages.text: Show that $g$ is injective
negative_passages.docid: 34260
negative_passages.text: Injective function from $\mathbb{R}^2$ to $\mathbb{R}$?
negative_passages.docid: 141166
negative_passages.text: How to show that when the linear transformation $\Phi =\psi \circ \phi : E \rightarrow G$ is injective, then $\phi$ is also injective?
negative_passages.docid: 117793
negative_passages.text: Finding a function $\mathbb{N} \to \mathbb{N}$ that is surjective but not injective.
negative_passages.docid: 11813
negative_passages.text: Injective functions also surjective?
negative_passages.docid: 141799
negative_passages.text: Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
negative_passages.docid: 119702
negative_passages.text: Showing a bijection between the set of ringhomomorphisms $\mathbb{Z}[i] \to R$ and the set of $x \in R$ for which $x^2+1=0$
negative_passages.docid: 27188
negative_passages.text: Bijection between $\mathbb{R}$ and $\mathbb{R}/\mathbb{Q}$
negative_passages.docid: 72644
negative_passages.text: Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
negative_passages.docid: 124847
negative_passages.text: Is the set of surjective functions from $\mathbb{N}$ to $\mathbb{N}$ uncountable?
negative_passages.docid: 41783
negative_passages.text: Cardinality of the Cartesian Product of Two Equinumerous Infinite Sets
negative_passages.docid: 73927
negative_passages.text: Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
negative_passages.docid: 152613
negative_passages.text: Injection from $\mathbb{N}\to\{0,1\}$ to the set of all monotonic decreasing functions from $\mathbb{N}\to\mathbb{Z}$
negative_passages.docid: 145077
negative_passages.text: A continuous bijection $f:\mathbb{R}\to \mathbb{R}$ is an homeomorphism?
negative_passages.docid: 136106
negative_passages.text: Is every open subset of $ \mathbb{R} $ uncountable?