query: Proving two sets are Equinumerous
positive_passages.docid: 10458
positive_passages.text: How to define a bijection between $(0,1)$ and $(0,1]$?
negative_passages.docid: 13167
negative_passages.text: Prove $A = (A \setminus B) \cup (A \cap B)$
negative_passages.docid: 121469
negative_passages.text: Proof of observations on natural numbers being expressed as differences of squares.
negative_passages.docid: 112084
negative_passages.text: Proof of a formula for the power set of a union of two sets
negative_passages.docid: 111032
negative_passages.text: Proof of Sets involving the Cartesian Product
negative_passages.docid: 142993
negative_passages.text: Proof of A ⊆ C and B ⊆ C ⇔ A ∪ B ⊆ C
negative_passages.docid: 64656
negative_passages.text: how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
negative_passages.docid: 1821
negative_passages.text: Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
negative_passages.docid: 39708
negative_passages.text: Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
negative_passages.docid: 113083
negative_passages.text: How to prove a set equality?
negative_passages.docid: 60359
negative_passages.text: Proving that these two sets are denumerable.
negative_passages.docid: 126015
negative_passages.text: Elementary number theory in sets
negative_passages.docid: 54496
negative_passages.text: Showing that $\mathbb{R}$ and $\mathbb{R}\backslash\mathbb{Q}$ are equinumerous using Cantor-Bernstein
negative_passages.docid: 86263
negative_passages.text: How do we show there are the same number of elements in each of the sets?
negative_passages.docid: 22482
negative_passages.text: How can an ordered pair be expressed as a set?
negative_passages.docid: 49709
negative_passages.text: Suppose $X$ is infinite and $A$ is a finite subset of $X$. Then $X$ and $X \setminus A$ are equinumerous
negative_passages.docid: 1627
negative_passages.text: Cartesian product of an arbitrary number of sets