query: Prove $X$ is uncountable if $X$ is the set of all functions $f: \mathbb{Z}_+ \rightarrow \mathbb{Z}_+$
positive_passages.docid: 21431
positive_passages.text: The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?
negative_passages.docid: 71922
negative_passages.text: Prove Uncountable set minus a countable set is uncountable
negative_passages.docid: 22391
negative_passages.text: Is the set of all pairs of real numbers uncountable?
negative_passages.docid: 155777
negative_passages.text: Show that infinite Cartesian product is uncountable
negative_passages.docid: 104842
negative_passages.text: Let $X$ be uncountable. Then the set of injective functions $f\colon X \to \mathbb{R}$ has empty interior in $\mathscr{C}(X;\mathbb{R})$
negative_passages.docid: 57021
negative_passages.text: Is the set of all functions $f:Z_+\rightarrow Z_+$ that are eventually constant countable.
negative_passages.docid: 91947
negative_passages.text: Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
negative_passages.docid: 139247
negative_passages.text: Real Analysis - Prove a set is countable
negative_passages.docid: 135694
negative_passages.text: Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
negative_passages.docid: 114770
negative_passages.text: Proof that a perfect set is uncountable
negative_passages.docid: 10431
negative_passages.text: Prove that $C\exp(x)$ is the only set of functions for which $f(x) = f'(x)$
negative_passages.docid: 156356
negative_passages.text: Proof that $x^n+\frac{1}{x^n}\in \mathbb Z$ by complete induction
negative_passages.docid: 109638
negative_passages.text: Show that a complete metric space without isolated points is uncountable
negative_passages.docid: 14277
negative_passages.text: Proving $f(x)=x\cdot |x|$ is a bijection
negative_passages.docid: 3636
negative_passages.text: Are any two uncountable sets similar to each other?
negative_passages.docid: 146436
negative_passages.text: Cardinality of the set of bijective functions on $\mathbb{N}$?
negative_passages.docid: 23442
negative_passages.text: Cardinality of the union of infinite and countable sets