query: Prove the equivalence of [-1,4) ~(2,11)
positive_passages.docid: 10458
positive_passages.text: How to define a bijection between $(0,1)$ and $(0,1]$?
negative_passages.docid: 41571
negative_passages.text: Prove that in a sequence of numbers $49 , 4489 , 444889 , 44448889\ldots$
negative_passages.docid: 136459
negative_passages.text: Prove ${n - 1 \choose k - 1} + {n - 2 \choose k - 1} + {n - 3 \choose k - 1} + \dots + {k - 1 \choose k - 1} = {n \choose k}$
negative_passages.docid: 78463
negative_passages.text: Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$
negative_passages.docid: 44689
negative_passages.text: Explicit bijection between $[0,1)$ and $(0,1)$
negative_passages.docid: 18914
negative_passages.text: How prove this $A=\left(B-\frac{1}{110}I\right)^T\left(B+\frac{1}{110}I\right)$
negative_passages.docid: 134075
negative_passages.text: Inverse of $A^{-1}+B^{-1}$
negative_passages.docid: 69833
negative_passages.text: Number of elements not equal to their inverses is even number
negative_passages.docid: 73002
negative_passages.text: For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$
negative_passages.docid: 121706
negative_passages.text: Show $\text{det}(A)$ is divisible by $2^{n-1}$
negative_passages.docid: 40763
negative_passages.text: Possible orders of permutations of $11$ symbols
negative_passages.docid: 141909
negative_passages.text: Prove ${2}^{n}\cdot(2m+1)-1 $ is invertible
negative_passages.docid: 105425
negative_passages.text: The intervals $(2,4)$ and $(-1,17)$ have the same cardinality
negative_passages.docid: 128415
negative_passages.text: Prove that $1<\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\dots+\frac{1}{3001}<\frac43$
negative_passages.docid: 98855
negative_passages.text: Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
negative_passages.docid: 26741
negative_passages.text: How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
negative_passages.docid: 14559
negative_passages.text: Binomial[-1,-1]