query: Existence of surjection implies existence of injection?
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: 24828
negative_passages.text: surjective immersion $\mathbb{R}^2 \to \mathbb{R}^2$ which is not a diffeomorphism
negative_passages.docid: 88201
negative_passages.text: Suppose $X$ is a finite set and $f : X \to X$ is a function. Then $f$ is injective if and only if $f$ is surjective.
negative_passages.docid: 100134
negative_passages.text: Proving existence of a surjection $2^{\aleph_0} \to \aleph_1$ without AC
negative_passages.docid: 5635
negative_passages.text: How to prove that the Frobenius endomorphism is surjective?
negative_passages.docid: 45380
negative_passages.text: Surjectivity implies injectivity and conversely
negative_passages.docid: 94165
negative_passages.text: Why is a map to a smaller dimensional space not injective?
negative_passages.docid: 11202
negative_passages.text: If $g \circ f$ is injective, so is $g$
negative_passages.docid: 2072
negative_passages.text: Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
negative_passages.docid: 72115
negative_passages.text: Why isn't there a continuously differentiable surjection from $I \to I \times I$?
negative_passages.docid: 74453
negative_passages.text: Injective and Surjective Functions
negative_passages.docid: 148500
negative_passages.text: Understanding this theorem and how to go about proving it surjectivity?
negative_passages.docid: 84301
negative_passages.text: Showing that some Function on the Unit Disc is injective
negative_passages.docid: 158078
negative_passages.text: Is linear surjective isometry always unitary?
negative_passages.docid: 35953
negative_passages.text: Prove that a function is not injective
negative_passages.docid: 48990
negative_passages.text: Linear map $f:V\rightarrow V$ injective $\Longleftrightarrow$ 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.