query: Let $f : N → Y$ be a map having right inverse $g$. Prove that $Y$ is at most countable?
positive_passages.docid: 16413
positive_passages.text: Proving existence of surjective $f:\mathbb{N} \rightarrow A$ implies $A$ is at most countable.
negative_passages.docid: 32774
negative_passages.text: Finite Cartesian Product of Countable sets is countable?
negative_passages.docid: 118595
negative_passages.text: Proving that a set is countable by finding a bijection
negative_passages.docid: 41617
negative_passages.text: If a $C^1$ map $f:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ is expanding ($\|f(x)-f(y)\|\geq\|x-y\|$), which of these must be true?
negative_passages.docid: 18223
negative_passages.text: Prove that the union of two disjoint countable sets is countable
negative_passages.docid: 94365
negative_passages.text: How to prove that if $D$ is countable, then $f(D)$ is either finite or countable?
negative_passages.docid: 84936
negative_passages.text: The set of all finite sequences of members of a countable set is also countable
negative_passages.docid: 148500
negative_passages.text: Understanding this theorem and how to go about proving it surjectivity?
negative_passages.docid: 88904
negative_passages.text: Help with a proof. Countable sets.
negative_passages.docid: 106606
negative_passages.text: How to prove that compact subspaces of the Sorgenfrey line are countable?
negative_passages.docid: 128437
negative_passages.text: How to prove that a finite set is countable
negative_passages.docid: 48009
negative_passages.text: Left inverse implies right inverse in a finite ring
negative_passages.docid: 116732
negative_passages.text: Proving that a continuous map is surjective
negative_passages.docid: 21243
negative_passages.text: Kaplansky's theorem of infinitely many right inverses in monoids?
negative_passages.docid: 45710
negative_passages.text: Finishing a proof: $f$ is injective if and only if it has a left inverse
negative_passages.docid: 66301
negative_passages.text: The cardinality of the set of countably infinite subsets of an infinite set
negative_passages.docid: 17997
negative_passages.text: Right identity and Right inverse implies a group