query: Show that the set $ M:= \{ A \subset \mathbb{N}: A $ has infinte many elements } countable is.
positive_passages.docid: 144787
positive_passages.text: Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
negative_passages.docid: 18223
negative_passages.text: Prove that the union of two disjoint countable sets is countable
negative_passages.docid: 2403
negative_passages.text: Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?
negative_passages.docid: 136006
negative_passages.text: Prove that any countable cartesian product of countable sets is countable
negative_passages.docid: 157513
negative_passages.text: How can I prove that these sets are countable infinite?
negative_passages.docid: 86685
negative_passages.text: Example of a set $S$ that is countable, but the set of limit points is uncountable
negative_passages.docid: 12472
negative_passages.text: Let $X$ and $Y$ be countable sets. Then $X\cup Y$ is countable
negative_passages.docid: 147136
negative_passages.text: Subset of a countable set is itself countable
negative_passages.docid: 40937
negative_passages.text: Is the set of partial order relations over $ \mathbb{N}$ countable?
negative_passages.docid: 79490
negative_passages.text: Proving the set of points at which a function diverges to $\infty$ is countable
negative_passages.docid: 125411
negative_passages.text: Infinite set always has a countably infinite subset
negative_passages.docid: 43268
negative_passages.text: How to prove that the set of rational numbers are countable?
negative_passages.docid: 132778
negative_passages.text: All distances are rational prove the set is countable
negative_passages.docid: 68139
negative_passages.text: Show that the set of polynomials with rational coefficients is countable.
negative_passages.docid: 23442
negative_passages.text: Cardinality of the union of infinite and countable sets
negative_passages.docid: 34998
negative_passages.text: How to prove that $\mathbb{Q}$ ( the rationals) is a countable set
negative_passages.docid: 16413
negative_passages.text: Proving existence of surjective $f:\mathbb{N} \rightarrow A$ implies $A$ is at most countable.