query: Prove that $\mathbb{R} \nsim \mathbb{R}^{\mathbb{R}}$.
positive_passages.docid: 13273
positive_passages.text: Cardinality of the set of all real functions of real variable
negative_passages.docid: 26497
negative_passages.text: Take $\mathbb{R}$ as a vector space over $\mathbb{Q}$, then a basis for $\mathbb{R}$, then $|B|=2^{\aleph_0}$
negative_passages.docid: 52902
negative_passages.text: How to prove $\int_{\mathbb R^d}{(1+|x|^{2})^{-m}dx}$ is integrable?
negative_passages.docid: 36996
negative_passages.text: If $x^{2}-x\in Z(R)$ for all $x\in R$, then $R$ is commutative.
negative_passages.docid: 124562
negative_passages.text: $f:\mathbb{R}^n \to \mathbb{R}$ has expansion $\sum_i g_i(x)x^i$
negative_passages.docid: 86054
negative_passages.text: $r+r^{-1}$ integral implies $r^n+r^{-n}$ integral
negative_passages.docid: 131082
negative_passages.text: Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic
negative_passages.docid: 66866
negative_passages.text: Algebraic dual of $\mathbb{R}^{\mathbb{N}}$
negative_passages.docid: 155579
negative_passages.text: Show that $End_A(A)$ = {$r_a$ | $a ∈ A$}
negative_passages.docid: 75059
negative_passages.text: Let $T:\mathbb{R}^n\to \mathbb{R}^n$ be a linear transformation...
negative_passages.docid: 53244
negative_passages.text: Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$
negative_passages.docid: 21553
negative_passages.text: Prove that $\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$
negative_passages.docid: 76148
negative_passages.text: Show that $\exists c \in \mathbb{R} : f(c) = 0$
negative_passages.docid: 37569
negative_passages.text: Prove that $\binom{n}{r} + \binom{n}{r+1} = \binom{n+1}{r+1} $
negative_passages.docid: 69166
negative_passages.text: Cardinality of $\mathbb{R}$ and $\mathbb{R}^2$
negative_passages.docid: 94580
negative_passages.text: Prove that, $\binom{3n}{r}=\binom{3n-1}{r} + \binom{3n-1}{r-1}$
negative_passages.docid: 94383
negative_passages.text: Prove that $A^TD-C^TB=I$