query: Trouble proving that $\mathbb{R} \approx \textbf{I} $
positive_passages.docid: 156783
positive_passages.text: $\mathbb R$ has the same cardinality of any interval
negative_passages.docid: 92289
negative_passages.text: Proof that Radius of Convergence Extend to Nearest Singularity
negative_passages.docid: 101329
negative_passages.text: Avoiding numerical cancellation question for $\sin x -\sin y$ for $x \approx y$
negative_passages.docid: 43282
negative_passages.text: Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
negative_passages.docid: 88971
negative_passages.text: An approximate eigenvalue for $ T \in B(X) $.
negative_passages.docid: 36747
negative_passages.text: $\text{Tor}_0^R(M,N)\simeq M\otimes_R N$
negative_passages.docid: 30330
negative_passages.text: How can I prove that this function is bounded using the given 2 hints?
negative_passages.docid: 66272
negative_passages.text: Is there a common notion of $\mathbb{R}^n$, for non-integer $n$?
negative_passages.docid: 27564
negative_passages.text: Prove that $\|UVU^{-1}V^{-1}-I\|\leq 2\|U-I\|\|V-I\|$
negative_passages.docid: 150572
negative_passages.text: Explicit norm on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$
negative_passages.docid: 141286
negative_passages.text: When is $\mathbf{X}^{T}\mathbf{X}+\lambda\mathbf{I}$ invertible?
negative_passages.docid: 153886
negative_passages.text: Existence of antiderivative on a part $I$ of $\mathbb{R}$
negative_passages.docid: 49240
negative_passages.text: $\forall x,y \in \mathbb{R}:\vert\cos x- \cos y\vert\leq\vert x-y\vert$
negative_passages.docid: 90540
negative_passages.text: What is wrong in this proof: That $\mathbb{R}$ has measure zero
negative_passages.docid: 117419
negative_passages.text: Why is $e^{x}$ not uniformly continuous on $\mathbb{R}$?
negative_passages.docid: 117533
negative_passages.text: $|A-\lambda I|$ and $|\lambda I-A|$
negative_passages.docid: 66239
negative_passages.text: Verifying that a certain collection of intervals of $\mathbb R$ forms a topology