query: $|A|\ge |B|$ iff there is a surjection $g:A\to B$
positive_passages.docid: 40586
positive_passages.text: There exists an injection from $X$ to $Y$ if and only if there exists a surjection from $Y$ to $X$.
negative_passages.docid: 134104
negative_passages.text: Is there a Cantor-Schroder-Bernstein statement about surjective maps?
negative_passages.docid: 72642
negative_passages.text: Continuous bijection from $(a,b) \to S^1$?
negative_passages.docid: 63146
negative_passages.text: Proof of properties of injective and surjective functions.
negative_passages.docid: 83996
negative_passages.text: For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$
negative_passages.docid: 148500
negative_passages.text: Understanding this theorem and how to go about proving it surjectivity?
negative_passages.docid: 40993
negative_passages.text: Let $f:G\to G'$ be a surjective homomorphism. Prove that if $G$ is cyclic, then $G'$ is cyclic.
negative_passages.docid: 138707
negative_passages.text: show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
negative_passages.docid: 158355
negative_passages.text: If $A$ commutes with $B$ and $B$ commutes with $C$, then $A$ commutes with $C$
negative_passages.docid: 62454
negative_passages.text: Let $f : G → G_1$ be a surjective homomorphism (also called epimorphism) from $G$ to another group $G_1$. Prove that $f(Z(G)) \subseteq Z(G_1)$.
negative_passages.docid: 148731
negative_passages.text: Constructing a bijection between $[a,b)$ to $(0,1)$
negative_passages.docid: 53971
negative_passages.text: If $g:V \rightarrow V$ is an injective linear transformation. Prove if $V$ is finite dimensional then $g$ is surjective.
negative_passages.docid: 121395
negative_passages.text: Let $X$ and $Y$ be non-empty sets and let $f:X \rightarrow Y$. Prove that $ f^{ −1} :P(Y ) → P(X) $ is injective if, and only if, $f$ is surjective.
negative_passages.docid: 56413
negative_passages.text: $f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
negative_passages.docid: 127488
negative_passages.text: If $L:\mathbb{R}^n \rightarrow \mathbb{R}^m$ and $m<n$ linear trans. What does this tell about injectivity and surjectivity?
negative_passages.docid: 76674
negative_passages.text: Let $S:U\rightarrow V, \ T:V\rightarrow W$ and if $S$ and $T$ are both injective/surjective, is $T\circ S$ injective/surjective?
negative_passages.docid: 133699
negative_passages.text: Proving that there is a bijection between $A$ and $B$.