query: If $\sum_{x \in X} f(x) < {\infty}$ then the set $\{x | f(x) \neq 0 \}$ is countable
positive_passages.docid: 20713
positive_passages.text: The sum of an uncountable number of positive numbers
negative_passages.docid: 21431
negative_passages.text: The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?
negative_passages.docid: 19297
negative_passages.text: Is the cofinite topology on an uncountable set first countable?
negative_passages.docid: 152563
negative_passages.text: Set of discontinuity of monotone function is countable
negative_passages.docid: 75019
negative_passages.text: Infinite Cartesian product of countable sets is uncountable
negative_passages.docid: 3772
negative_passages.text: About the continuity of the function $f(x) = \sum\limits_k2^{-k}\mathbf 1_{q_k \leq x}$
negative_passages.docid: 12472
negative_passages.text: Let $X$ and $Y$ be countable sets. Then $X\cup Y$ is countable
negative_passages.docid: 41192
negative_passages.text: Neatest proof that set of finite subsets is countable?
negative_passages.docid: 155168
negative_passages.text: Is the collection of finite subsets of $\mathbb{Z}$ countable?
negative_passages.docid: 88904
negative_passages.text: Help with a proof. Countable sets.
negative_passages.docid: 68994
negative_passages.text: Countable closed sets
negative_passages.docid: 5105
negative_passages.text: Alternative definition of $\|f\|_{\infty}$ as the smallest of all numbers of the form $\sup\{|g(x)| : x \in X \}$, where $f = g$ almost everywhere
negative_passages.docid: 102113
negative_passages.text: Proof that the number of proofs is countably infinite
negative_passages.docid: 134844
negative_passages.text: Summablity and countability
negative_passages.docid: 92588
negative_passages.text: Showing that $(C_0([0,\infty)), \|\cdot\|_\infty)$ is complete.
negative_passages.docid: 6523
negative_passages.text: Prove that the space has a countable dense subset
negative_passages.docid: 28007
negative_passages.text: Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $