query: Showing that $\sigma$-algebra is uncountable
positive_passages.docid: 146006
positive_passages.text: Uncountable $\sigma$-algebra
negative_passages.docid: 38946
negative_passages.text: Show that $\{\cup_{n\in K} (n, n+1]: K \subset \mathbb{Z}\}$ is a $\sigma$-algebra on $\mathbb{R}$
negative_passages.docid: 153542
negative_passages.text: Fixed Field of $\sigma, \tau$
negative_passages.docid: 72750
negative_passages.text: Uncountable number of mutually disjoint countable sets in $\mathbb R$
negative_passages.docid: 51134
negative_passages.text: If $E \in \sigma(\mathcal{C})$ then there exists a countable subset $\mathcal{C}_0 \subseteq \mathcal{C}$ with $E \in \sigma(\mathcal{C}_0)$
negative_passages.docid: 10702
negative_passages.text: Show that $\left\{A\subset\Omega: A~\text{ is countable or }A^C\text{ is countable}\right\}$ is a $\sigma$-algebra
negative_passages.docid: 113668
negative_passages.text: Uncountable chain of subsets of $\mathbb N$
negative_passages.docid: 73869
negative_passages.text: $\mathcal{C}_1 \subseteq \mathcal{C}_2 \implies \sigma( \mathcal{C}_1) \subseteq \sigma( \mathcal{C}_2) $
negative_passages.docid: 83116
negative_passages.text: Uncountability of basis of $\mathbb R^{\mathbb N}$
negative_passages.docid: 32965
negative_passages.text: Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
negative_passages.docid: 147783
negative_passages.text: Showing a sigma algebra is the union of certain collection of sigma algebras
negative_passages.docid: 116676
negative_passages.text: Examples of uncountable sets with zero Lebesgue measure
negative_passages.docid: 53399
negative_passages.text: Proof of the uncountability of reals using the diagonal argument—problem?
negative_passages.docid: 64118
negative_passages.text: Number of elements in a finite $\sigma$-algebra
negative_passages.docid: 71922
negative_passages.text: Prove Uncountable set minus a countable set is uncountable
negative_passages.docid: 90749
negative_passages.text: Show that $\sum\nolimits_{d|n} \frac{1}{d} = \frac{\sigma (n)}{n}$ for every positive integer $n$.
negative_passages.docid: 86685
negative_passages.text: Example of a set $S$ that is countable, but the set of limit points is uncountable