query: Least Upper Bound Proof
positive_passages.docid: 143130
positive_passages.text: Proving that the supremum of $(a,b)$ is $b$.
negative_passages.docid: 17159
negative_passages.text: Proof of Closest Point Theorem in Hilbert Space
negative_passages.docid: 148376
negative_passages.text: Proving that a Binary Tree of $n$ nodes has a height of at least $\log(n)$.
negative_passages.docid: 120309
negative_passages.text: Number Theory Inequality Proof
negative_passages.docid: 77192
negative_passages.text: How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?
negative_passages.docid: 131559
negative_passages.text: Lower Bound of Central Binomial Coefficients
negative_passages.docid: 20040
negative_passages.text: shorter proof of generalized mediant inequality?
negative_passages.docid: 28006
negative_passages.text: The minimum of two independent geometric random variables
negative_passages.docid: 145447
negative_passages.text: bilinear form - proof
negative_passages.docid: 81767
negative_passages.text: Reverse Markov Inequality for non-negative unbounded random variables
negative_passages.docid: 138316
negative_passages.text: A simple inequality for floor function
negative_passages.docid: 86635
negative_passages.text: Optimizing $(X_{n}+c)^{2}$ to show that $P(\overline{X}_{n}\geq \lambda) \leq E(X_{n}^{2})/(EX_{n}^{2}+ \lambda^{2})$
negative_passages.docid: 6874
negative_passages.text: smallest value of $k$ for which $a_k$ is $0$
negative_passages.docid: 86518
negative_passages.text: Does $X$ have a lower bound?
negative_passages.docid: 44817
negative_passages.text: Lower bound on energy is potential minimum
negative_passages.docid: 117262
negative_passages.text: Proving a logarithm inequality
negative_passages.docid: 16392
negative_passages.text: Prove the Inequality on sequence