query: Lemma for a question based on Greatest Integer function
positive_passages.docid: 133755
positive_passages.text: Is true that $\sum_{k=1}^n\frac{[kx]}{k}\leq[nx]$, for every $x\in\mathbb{R}$ and for every $n\in\mathbb{Z}^+$?
negative_passages.docid: 113182
negative_passages.text: Applying Zorn's lemma
negative_passages.docid: 117262
negative_passages.text: Proving a logarithm inequality
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: 83036
negative_passages.text: f(g(x)) has a degree divisible by n
negative_passages.docid: 48679
negative_passages.text: measurability of supremum of a class of functions
negative_passages.docid: 47611
negative_passages.text: Integers and integer functions
negative_passages.docid: 45460
negative_passages.text: Proof verification of a number theory problem involving sequences.
negative_passages.docid: 127634
negative_passages.text: query on maximum minimum of multi-variable function
negative_passages.docid: 101619
negative_passages.text: Question involving the Cauchy-Goursat Theorem
negative_passages.docid: 121406
negative_passages.text: Interesting Integration with respect to $[x]$ where $[\cdot]$ is greatest integer function
negative_passages.docid: 84394
negative_passages.text: Choice function for a collection of nonempty subsets of $\{0,1\}^\omega$
negative_passages.docid: 148470
negative_passages.text: bound of the function
negative_passages.docid: 59535
negative_passages.text: Prove that there exists such a set of $n$ positive integers
negative_passages.docid: 35644
negative_passages.text: Find the supremum of the following set
negative_passages.docid: 127426
negative_passages.text: Greatest number in the sequence
negative_passages.docid: 63710
negative_passages.text: For x < 5 what is the greatest value of x