query: Cardinality of a subset of $A$ without elements $x = 2y$
positive_passages.docid: 142886
positive_passages.text: Find set with maximal cardinality given constraints
negative_passages.docid: 121366
negative_passages.text: Intervals and cardinality
negative_passages.docid: 101669
negative_passages.text: Cardinality of the Set of all finite subset of $\mathbb{R}$
negative_passages.docid: 146098
negative_passages.text: Number of nonempty subsets of a set with $n$ elements
negative_passages.docid: 82628
negative_passages.text: Cardinality of a set of closed intervals
negative_passages.docid: 70164
negative_passages.text: Proof exercise that the cardinal number of a set in $\mathbb R^2$ is $\frak c$
negative_passages.docid: 150790
negative_passages.text: Prove two sets have same Cardinality by writing down bijection
negative_passages.docid: 102972
negative_passages.text: Cardinality of $\mathbb{R}^\mathbb{R}$ by diagonal argument
negative_passages.docid: 131983
negative_passages.text: Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
negative_passages.docid: 146664
negative_passages.text: The union of two linearly independent subsets
negative_passages.docid: 102136
negative_passages.text: How many subsets contain no consecutive elements?
negative_passages.docid: 3072
negative_passages.text: If the empty set is a subset of every set, why isn't $\{\emptyset,\{a\}\}=\{\{a\}\}$?
negative_passages.docid: 6291
negative_passages.text: Proving something is a linearly independent subset
negative_passages.docid: 69166
negative_passages.text: Cardinality of $\mathbb{R}$ and $\mathbb{R}^2$
negative_passages.docid: 156006
negative_passages.text: Cardinality of set containing all infinite subsets of $\mathbb{Q}$
negative_passages.docid: 73850
negative_passages.text: Cardinality of set of functions
negative_passages.docid: 90826
negative_passages.text: Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly