query: If there is a surjection $A\to B $ and another $B\to A$ then $A $ and $B$ are in bijection
positive_passages.docid: 134104
positive_passages.text: Is there a Cantor-Schroder-Bernstein statement about surjective maps?
negative_passages.docid: 134914
negative_passages.text: Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
negative_passages.docid: 104757
negative_passages.text: If $f \circ g$ is surjective, then f is surjective
negative_passages.docid: 155545
negative_passages.text: Showing that $a \mid b$ and $b \mid a$ if and only if $a= \pm b$.
negative_passages.docid: 130363
negative_passages.text: Prove composition of two surjections is surjection
negative_passages.docid: 21707
negative_passages.text: Constructing a Bijective function via an injective and surjective one.
negative_passages.docid: 27188
negative_passages.text: Bijection between $\mathbb{R}$ and $\mathbb{R}/\mathbb{Q}$
negative_passages.docid: 6023
negative_passages.text: Surjectivity of Composition of Surjective Functions
negative_passages.docid: 148500
negative_passages.text: Understanding this theorem and how to go about proving it surjectivity?
negative_passages.docid: 63267
negative_passages.text: Under what conditions on the sets $A$ and $B$ will it be true that $A\times B= B\times A$
negative_passages.docid: 93964
negative_passages.text: Proving that $f$ is a bijection from $N$x$N$ to $N$.
negative_passages.docid: 90566
negative_passages.text: There exists surjections from A onto B and vice versa, and there is no bijection between the sets?
negative_passages.docid: 97878
negative_passages.text: Are there uncountably many surjections from $\mathbb N$ to $\mathbb N$?
negative_passages.docid: 3323
negative_passages.text: Bijection Contruction
negative_passages.docid: 148731
negative_passages.text: Constructing a bijection between $[a,b)$ to $(0,1)$
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: 64583
negative_passages.text: Number of surjective functions from A to B