query: Proving cardinality given surjection from A to B and B to A
positive_passages.docid: 146356
positive_passages.text: To prove two sets are isomorphic is it sufficient to find 2 injections or 2 surjections?
negative_passages.docid: 72642
negative_passages.text: Continuous bijection from $(a,b) \to S^1$?
negative_passages.docid: 83518
negative_passages.text: Proving Two sets have same cardinality
negative_passages.docid: 27188
negative_passages.text: Bijection between $\mathbb{R}$ and $\mathbb{R}/\mathbb{Q}$
negative_passages.docid: 69166
negative_passages.text: Cardinality of $\mathbb{R}$ and $\mathbb{R}^2$
negative_passages.docid: 23125
negative_passages.text: Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
negative_passages.docid: 111954
negative_passages.text: Computing the cardinality of a combinatorial set
negative_passages.docid: 72591
negative_passages.text: Find a bijection to prove a fact about integer partitions
negative_passages.docid: 28391
negative_passages.text: Prove the compactness of a set B
negative_passages.docid: 13136
negative_passages.text: Element chasing proof that $(A\setminus C)\setminus(B\setminus C) = (A\setminus B)\setminus C$
negative_passages.docid: 47434
negative_passages.text: Proof that $A \subseteq B \Leftrightarrow A \cup B = B$
negative_passages.docid: 44689
negative_passages.text: Explicit bijection between $[0,1)$ and $(0,1)$
negative_passages.docid: 116732
negative_passages.text: Proving that a continuous map is surjective
negative_passages.docid: 100134
negative_passages.text: Proving existence of a surjection $2^{\aleph_0} \to \aleph_1$ without AC
negative_passages.docid: 130363
negative_passages.text: Prove composition of two surjections is surjection
negative_passages.docid: 37951
negative_passages.text: proof detail concerning bijection between a set and its power set
negative_passages.docid: 15733
negative_passages.text: Show that the cardinality of $\mathbb N$ is the same as the cardinality of $\mathbb N \times \mathbb N$