query: Finding an injection $f:\mathcal{P}(\mathbb{N})\rightarrow\mathbb{R}$
positive_passages.docid: 41052
positive_passages.text: The set of real numbers and power set of the natural numbers
negative_passages.docid: 118049
negative_passages.text: Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
negative_passages.docid: 110885
negative_passages.text: Does there exists a continuous surjection from $\mathbb{R}$ to $\mathbb{R}^2$?
negative_passages.docid: 139537
negative_passages.text: Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
negative_passages.docid: 63701
negative_passages.text: An example of a regular function over an open set
negative_passages.docid: 55488
negative_passages.text: Proving that $\operatorname{codim}(X,Y)=\dim(\mathcal{O}_{X,\eta})$
negative_passages.docid: 153612
negative_passages.text: Finding $g_i:\mathbb{R}^n\to\mathbb R$ s.t $f(x)=\sum\limits_{i=1}^nx_i\cdot g_i(x)$
negative_passages.docid: 146356
negative_passages.text: To prove two sets are isomorphic is it sufficient to find 2 injections or 2 surjections?
negative_passages.docid: 110014
negative_passages.text: Right Inverse for Surjective Function
negative_passages.docid: 45342
negative_passages.text: Generalization of Mean Value Theorem to functions, $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$
negative_passages.docid: 28798
negative_passages.text: Proving injection and surjection with functions $F:C^B\to C^A$, $F(f)=f\circ\varphi$, $\varphi: A\to B$
negative_passages.docid: 43907
negative_passages.text: Contraction mapping in the context of $f(x_n)=x_{n+1}$.
negative_passages.docid: 25260
negative_passages.text: Extension of a morphism $k^*\rightarrow X$ to $\mathbb{P}^1\rightarrow \overline{X}$
negative_passages.docid: 25795
negative_passages.text: Density of $\mathbb{Q}^n$ in $\mathbb{R}^n$
negative_passages.docid: 155266
negative_passages.text: Is $\exp:\overline{\mathbb{M}}_n\to\mathbb{M}_n$ injective?
negative_passages.docid: 131530
negative_passages.text: Derivative of a pure function with SlotSequence
negative_passages.docid: 93806
negative_passages.text: $\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$