List questions from ceiling-and-floor-functions

Published on 11 Jun 2020 - 19:55

117

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Integral of a floor function.

Published on 12 Jun 2020 - 3:40

47

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Evaluate $\int_{-1}^{3} [ x+ \frac{1}{2}] dx$

Published on 12 Jun 2020 - 16:02

58

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If $\xi:[0,1]\to[0,1)$ is decreasing, is $[0,\infty)\ni t\mapsto\xi(1)^{\lfloor t\rfloor}\xi(x-\lfloor x\rfloor)$ eventually nonincreasing?

Published on 27 Mar 2026 - 4:23

238

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Last two digits of $[(\sqrt{5}+2)^{2016}]$

Published on 13 Jun 2020 - 14:31

122

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Compute $\sum_{i=0}^{100}\lfloor i^{3/2}\rfloor+\sum_{j=0}^{1000}\lfloor i^{2/3}\rfloor$

Published on 14 Jun 2020 - 5:03

78

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Evaluate $ \lim _{x \rightarrow 0}\left(x^{2}\left(1+2+3+\dots+\left[\frac{1}{|x|}\right]\right)\right) $

Published on 15 Jun 2020 - 17:14

72

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Find all nonconstant polynomials P such that P({X})={P(X)}

Published on 16 Jun 2020 - 5:25

52

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Ceil and Floor functions on fractions

Published on 17 Jun 2020 - 10:28

517

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What does $[5.9]$ mean?

Published on 17 Jun 2020 - 18:32

42

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Why does this relation $\sum ^{k}_{n=m} f( n) =\int\limits ^{k+1}_{m} f(\lfloor x\rfloor ) dx$ not apply here?

Published on 20 Jun 2020 - 18:37

180

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Pairwise disjoint sets of the form $\{\lfloor n\alpha \rfloor : n \in \mathbb{N}\}.$

Published on 21 Jun 2020 - 11:30

118

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an identity involving the floor function.

Published on 25 Jun 2020 - 2:04

61

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For a fixed $k$ what is the value of $\sum_{l=1}^{5^m-1} \Big\lfloor \dfrac{l}{5^k}\Big \rfloor$

Published on 25 Jun 2020 - 20:09

136

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Floor function parity problem

Published on 26 Mar 2026 - 6:17

List Question

Looking for a formula to compute $\left\lceil \frac{x+1}{2} \right\rceil$

Integral of a floor function.

Evaluate $\int_{-1}^{3} [ x+ \frac{1}{2}] dx$

If $\xi:[0,1]\to[0,1)$ is decreasing, is $[0,\infty)\ni t\mapsto\xi(1)^{\lfloor t\rfloor}\xi(x-\lfloor x\rfloor)$ eventually nonincreasing?

Last two digits of $[(\sqrt{5}+2)^{2016}]$

Compute $\sum_{i=0}^{100}\lfloor i^{3/2}\rfloor+\sum_{j=0}^{1000}\lfloor i^{2/3}\rfloor$

Evaluate $ \lim _{x \rightarrow 0}\left(x^{2}\left(1+2+3+\dots+\left[\frac{1}{|x|}\right]\right)\right) $

Find all nonconstant polynomials P such that P({X})={P(X)}

Ceil and Floor functions on fractions

What does $[5.9]$ mean?

Why does this relation $\sum ^{k}_{n=m} f( n) =\int\limits ^{k+1}_{m} f(\lfloor x\rfloor ) dx$ not apply here?

Pairwise disjoint sets of the form $\{\lfloor n\alpha \rfloor : n \in \mathbb{N}\}.$

an identity involving the floor function.

For a fixed $k$ what is the value of $\sum_{l=1}^{5^m-1} \Big\lfloor \dfrac{l}{5^k}\Big \rfloor$

Floor function parity problem

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