query: Does $f$ have to be injective or surjective?
positive_passages.docid: 145439
positive_passages.text: Function with inputs moved from each other for a distance less than $a$
negative_passages.docid: 105455
negative_passages.text: Prove that "injective function $f:X\to Y$ exists" and "surjective function $g:Y\to X$ exists" is logically equivalent.
negative_passages.docid: 80626
negative_passages.text: Is this an equivalent formulation of "surjective" resp. "epimorphism"?
negative_passages.docid: 22061
negative_passages.text: $|f(x)-f(y)|\geq k|x-y|$.Then $f$ is bijective and its inverse is continuous.
negative_passages.docid: 20199
negative_passages.text: Find a surjective function $f:\mathbb{N}\to \mathbb{Q}$
negative_passages.docid: 112807
negative_passages.text: Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
negative_passages.docid: 40415
negative_passages.text: Why do we require quotient to be surjective?
negative_passages.docid: 148500
negative_passages.text: Understanding this theorem and how to go about proving it surjectivity?
negative_passages.docid: 53551
negative_passages.text: $f(A\cap B)=f(A)\cap f(B)$ $\iff$ $f$ is injective.
negative_passages.docid: 21707
negative_passages.text: Constructing a Bijective function via an injective and surjective one.
negative_passages.docid: 642
negative_passages.text: Does a surjective ring homomorphism have to be surjective on the unit groups?
negative_passages.docid: 122814
negative_passages.text: Finite Sets, Equal Cardinality, Injective $\iff$ Surjective.
negative_passages.docid: 53168
negative_passages.text: Surjective, Injective, Bijective Functions from $\mathbb Z$ to itself
negative_passages.docid: 33489
negative_passages.text: |f| is periodic implies f is periodic
negative_passages.docid: 45792
negative_passages.text: Rigorous proof that surjectivity implies injectivity for finite sets
negative_passages.docid: 142845
negative_passages.text: is $y = \sqrt{x^2 + 1}− x$ a injective (one-to-one) function?
negative_passages.docid: 146188
negative_passages.text: Why does a proof of $\exists f: X\to Y$ injection $\iff \exists g: Y \to X$ surjection requires the axiom of choice?