query: How to show that a set with injections into and from $\mathbb{N}$ is uncountable?
positive_passages.docid: 146055
positive_passages.text: Proving a set of functions is uncountable
negative_passages.docid: 30587
negative_passages.text: Uncountable well ordered set in $Z^-$ theory.
negative_passages.docid: 76597
negative_passages.text: Examples of provably${}^n$ unprovable statements
negative_passages.docid: 129109
negative_passages.text: Is the set of polynomial with coefficients on $\mathbb{Q}$ enumerable?
negative_passages.docid: 53399
negative_passages.text: Proof of the uncountability of reals using the diagonal argument—problem?
negative_passages.docid: 40937
negative_passages.text: Is the set of partial order relations over $ \mathbb{N}$ countable?
negative_passages.docid: 83116
negative_passages.text: Uncountability of basis of $\mathbb R^{\mathbb N}$
negative_passages.docid: 132868
negative_passages.text: Bijection between an infinite set and its union of a countably infinite set
negative_passages.docid: 132382
negative_passages.text: Showing a set is nowhere dense in $C([0,1])$
negative_passages.docid: 46698
negative_passages.text: Showing a set is closed under inverses
negative_passages.docid: 110635
negative_passages.text: Proving $\mathbb{N}^k$ is countable
negative_passages.docid: 67064
negative_passages.text: Uncountable minus countable set is uncountable
negative_passages.docid: 60359
negative_passages.text: Proving that these two sets are denumerable.
negative_passages.docid: 139826
negative_passages.text: arbitrary large finite sums of an uncountable set.
negative_passages.docid: 128437
negative_passages.text: How to prove that a finite set is countable
negative_passages.docid: 9651
negative_passages.text: Cardinality of cartesian product of an infinite set with N
negative_passages.docid: 33157
negative_passages.text: Proof that an infinite subset of $\mathbb{N}$ is countable