query: Proof regarding finding the two sets $S$ and $T$ are equinumerous
positive_passages.docid: 10458
positive_passages.text: How to define a bijection between $(0,1)$ and $(0,1]$?
negative_passages.docid: 99376
negative_passages.text: Prove that If $m'$ is a common multiple of $s$ and $t$, then $m | m'$. Here $m$ is the LCM of $s$ and $t$.
negative_passages.docid: 13398
negative_passages.text: Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) \times (0, 1)$ have the same cardinality
negative_passages.docid: 101179
negative_passages.text: Partition of a set and Hall's theorem
negative_passages.docid: 112084
negative_passages.text: Proof of a formula for the power set of a union of two sets
negative_passages.docid: 88982
negative_passages.text: Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
negative_passages.docid: 66948
negative_passages.text: Proving question on sets
negative_passages.docid: 29065
negative_passages.text: Encode each $n_1,n_2,n_3,...∈N^N$ by an inﬁnite sequence of 0s and 1s with inﬁnitely many 0s, and give a proof that $N^N$ is equinumerous with $R$.
negative_passages.docid: 41477
negative_passages.text: Prove $f(S \cap T) \subseteq f(S) \cap f(T)$
negative_passages.docid: 134120
negative_passages.text: Prove statement with a counter-example: For all sets S, T and V, V ∪ (S ∩ T) = (V ∪ S) ∩ T is false
negative_passages.docid: 4912
negative_passages.text: Show that an infinite set $C$ is equipotent to its cartesian product $C\times C$
negative_passages.docid: 21820
negative_passages.text: How to prove that a set is invariant?
negative_passages.docid: 144266
negative_passages.text: set theory proof of $A\cap B = A \setminus(A\setminus B)$
negative_passages.docid: 28223
negative_passages.text: Prove/Disprove that if two sets have the same power set then they are the same set
negative_passages.docid: 33216
negative_passages.text: Prove that the order of an element in $S_n$ equals the least common multiple of the lengths of the cycles in its cycle decomposition.
negative_passages.docid: 77286
negative_passages.text: Proving set theory question
negative_passages.docid: 86263
negative_passages.text: How do we show there are the same number of elements in each of the sets?