query: How to prove there is no surjection $f\colon X \rightarrow 2^X$
positive_passages.docid: 20706
positive_passages.text: Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
negative_passages.docid: 61066
negative_passages.text: Prove: $(A\rightarrow B),(A\rightarrow C)\rightarrow B, \mapsto_{HPC} B $
negative_passages.docid: 106768
negative_passages.text: Recognizing that a function has no elementary antiderivative
negative_passages.docid: 63146
negative_passages.text: Proof of properties of injective and surjective functions.
negative_passages.docid: 128524
negative_passages.text: Proving there is no analytic function
negative_passages.docid: 136538
negative_passages.text: How can I show that a bijection between $[0,1)$ and $(0,1)$ cannot be continuous?
negative_passages.docid: 46748
negative_passages.text: If $g \circ f$ is surjective, show that $f$ does not have to be surjective?
negative_passages.docid: 110014
negative_passages.text: Right Inverse for Surjective Function
negative_passages.docid: 135606
negative_passages.text: No function $f:\mathbb{Z}\rightarrow \{1, 2, 3\}$ satisfying $f(x)\ne f(y)$ for all integers $x,y$ and $|x-y|\in\{2, 3, 5\}$
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?
negative_passages.docid: 125707
negative_passages.text: A simple proof (hopefully) for $2^x \neq 0$
negative_passages.docid: 149416
negative_passages.text: Show that $ \{\lnot,\leftrightarrow\} $ is not functional complete
negative_passages.docid: 14277
negative_passages.text: Proving $f(x)=x\cdot |x|$ is a bijection
negative_passages.docid: 95469
negative_passages.text: Suppose $f:[0,1] \Rightarrow \mathbb{R}$ is continuous and $\int_0^x f(x)dx = \int_x^1 f(x)dx$. Prove that $f(x) = 0$ for all $x$
negative_passages.docid: 143798
negative_passages.text: Prove that, there exists no continuous function $f:\mathbb R\rightarrow\mathbb R$ with $f=\chi_{[0,1]}$ almost everywhere.
negative_passages.docid: 94682
negative_passages.text: Polynomial: prove there is no double root
negative_passages.docid: 41201
negative_passages.text: How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.