query: Is $2^{\aleph_0}=c$?
positive_passages.docid: 20281
positive_passages.text: Easiest way to prove that $2^{\aleph_0} = c$
negative_passages.docid: 15626
negative_passages.text: Relations of a~b iff b = ak^2
negative_passages.docid: 151355
negative_passages.text: Are cardinal numbers well defined? Or could we have something like $\aleph_{1/2}$?
negative_passages.docid: 110944
negative_passages.text: Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
negative_passages.docid: 3902
negative_passages.text: Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
negative_passages.docid: 55062
negative_passages.text: $2\times 2$ matrix $C=AB-BA$
negative_passages.docid: 11069
negative_passages.text: Deciding whether $2^{\sqrt2}$ is irrational/transcendental
negative_passages.docid: 24572
negative_passages.text: Does $n \mid 2^{2^n+1}+1$ imply $n \mid 2^{2^{2^n+1}+1}+1$?
negative_passages.docid: 127378
negative_passages.text: Is $2^\alpha=2^\beta\Rightarrow \alpha=\beta$ a $\sf ZFC$-independence result?
negative_passages.docid: 90199
negative_passages.text: Prove that there exists a constant $c>0$ such that the following happens
negative_passages.docid: 43598
negative_passages.text: Do $\omega^\omega=2^{\aleph_0}=\aleph_1$?
negative_passages.docid: 18530
negative_passages.text: Given 4 integers, $a, b, c, d > 0$, does $\frac{a}{b} < \frac{c}{d}$ imply $\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$?
negative_passages.docid: 45555
negative_passages.text: $(x+y)^c\le x^c+y^c$ for $0<c\le1$
negative_passages.docid: 62977
negative_passages.text: Show on $\mathbb{N}$ there are $2^{\aleph_0}$ nonisomorphic linear orders.
negative_passages.docid: 158257
negative_passages.text: Is aleph-$0$ a natural number?
negative_passages.docid: 94383
negative_passages.text: Prove that $A^TD-C^TB=I$
negative_passages.docid: 79349
negative_passages.text: The Aleph numbers and infinity in calculus.