query: Summablity and countability
positive_passages.docid: 154225
positive_passages.text: How many positive numbers need to be added together to ensure that the sum is infinite?
negative_passages.docid: 94365
negative_passages.text: How to prove that if $D$ is countable, then $f(D)$ is either finite or countable?
negative_passages.docid: 153652
negative_passages.text: Countable ordinals are embeddable in the rationals $\Bbb Q$ -- proofs and their use of AC
negative_passages.docid: 12472
negative_passages.text: Let $X$ and $Y$ be countable sets. Then $X\cup Y$ is countable
negative_passages.docid: 85895
negative_passages.text: Proving all rational numbers including negatives are countable
negative_passages.docid: 32774
negative_passages.text: Finite Cartesian Product of Countable sets is countable?
negative_passages.docid: 63276
negative_passages.text: Is an arbitrary union of a chain of countable sets countable?
negative_passages.docid: 7723
negative_passages.text: Countable basis of function spaces
negative_passages.docid: 136321
negative_passages.text: Show that if $\sup\big\{\sum\lvert\, f(a)\rvert\big\}  0\}$ is countable.
negative_passages.docid: 23837
negative_passages.text: Why is $\mathbb{R}/{\sim}$ not first countable at $[0]$, where $x \sim y \Leftrightarrow x = y\text{ or }x,y \in \mathbb{Z}$?
negative_passages.docid: 102391
negative_passages.text: Abel summability under the hypothesis $a_n \ge 0$
negative_passages.docid: 154474
negative_passages.text: Image of countable and uncountable sets
negative_passages.docid: 36315
negative_passages.text: Is $[0,1]$ a countable disjoint union of closed sets?
negative_passages.docid: 80019
negative_passages.text: $\varepsilon$-number countability without choice
negative_passages.docid: 122506
negative_passages.text: Relation on countable sets
negative_passages.docid: 107172
negative_passages.text: Countable nouns and determiners
negative_passages.docid: 9021
negative_passages.text: An infinite subset of a countable set is countable