query: Proof that the function $f$ is not injective.
positive_passages.docid: 27265
positive_passages.text: Continuously differentiable map from $\mathbb{R}^{m+n}$ to $\mathbb{R}^n$
negative_passages.docid: 59063
negative_passages.text: $f(f(x))=f(x)$ question
negative_passages.docid: 70576
negative_passages.text: Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
negative_passages.docid: 3518
negative_passages.text: Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous
negative_passages.docid: 89514
negative_passages.text: Show that if $g \circ f$ is injective, then so is $f$.
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: 151575
negative_passages.text: Differentiable bijection $f:\mathbb{R} \to \mathbb{R}$ with nonzero derivative whose inverse is not differentiable
negative_passages.docid: 121771
negative_passages.text: Proof $f(x)\equiv 0$
negative_passages.docid: 35569
negative_passages.text: Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
negative_passages.docid: 146055
negative_passages.text: Proving a set of functions is uncountable
negative_passages.docid: 74453
negative_passages.text: Injective and Surjective Functions
negative_passages.docid: 123132
negative_passages.text: Counterexample for a non-measurable function?
negative_passages.docid: 134720
negative_passages.text: Show that there is no increasing function $f: \aleph_1 \to \mathbb{R}$
negative_passages.docid: 92703
negative_passages.text: Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.
negative_passages.docid: 83907
negative_passages.text: $f$ bounded but $f'$ isn't
negative_passages.docid: 75888
negative_passages.text: How to prove the function $y = \sin x$ is not a closed function?
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.