List questions from ceiling-and-floor-functions

Published on 31 Mar 2026 - 12:10

351

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How to integrate $\int\limits_0^1 \left(-1\right)^{^{\left\lfloor\frac{1}{x}\right\rfloor}} dx$?

Published on 23 Dec 2015 - 19:07

144

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Calculating the value of $\lfloor(1+\sqrt{2})^{2n}\rfloor$

Published on 28 Mar 2026 - 23:16

108

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Manual Graph Sketching For $\lfloor(x)\rfloor+\sqrt{x-\lfloor(x)\rfloor}$

Published on 28 Dec 2015 - 10:36

37

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Closed form expression for $n_j$ defined by $n_j=\lceil n_{j−1}/b\rceil$ clarification

Published on 29 Dec 2015 - 20:55

153

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Find $\lfloor z \rfloor $ given that $z=(\{\sqrt{3}\}^2-2\{\sqrt{2}\}^2)/(\{\sqrt{3}\}-2\{\sqrt{2}\})$

Published on 30 Dec 2015 - 14:29

74

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How to solve $n^2-n<\lfloor\frac{n^2}{4}\rfloor$ ,$n \in \mathbb{N}$?

Published on 04 Jan 2016 - 9:42

233

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Prove $\int_0^n \lfloor x\rfloor \,dx = \frac{n (n-1)}{2}$

Published on 06 Jan 2016 - 20:10

131

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The number of real roots of $x\lfloor x\rfloor+187=\lfloor x^{2}\rfloor+\lfloor x\rfloor$

Published on 08 Jan 2016 - 5:21

305

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Equation involving floor function:

Published on 08 Jan 2016 - 21:22

6.5k

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How to prove ceiling and floor inequality more 'formally'?

Published on 10 Jan 2016 - 4:25

84

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Possible circular reasoning in textbook proof that $\lceil x+m\rceil=\lceil x\rceil +m$

Published on 11 Jan 2016 - 4:16

641

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Conjectures Involving floor(x)/piecewise continuity with regards to Integration and Differential Equations

Published on 24 Mar 2026 - 2:47

2.5k

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ceiling functions inequality

Published on 13 Jan 2016 - 14:21

251

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Compute $\lim_{x\to 0}\frac{x}{[x]}$

Published on 13 Jan 2016 - 19:13

List Question

A valid floor function trick?

How to integrate $\int\limits_0^1 \left(-1\right)^{^{\left\lfloor\frac{1}{x}\right\rfloor}} dx$?

Calculating the value of $\lfloor(1+\sqrt{2})^{2n}\rfloor$

Manual Graph Sketching For $\lfloor(x)\rfloor+\sqrt{x-\lfloor(x)\rfloor}$

Closed form expression for $n_j$ defined by $n_j=\lceil n_{j−1}/b\rceil$ clarification

Find $\lfloor z \rfloor $ given that $z=(\{\sqrt{3}\}^2-2\{\sqrt{2}\}^2)/(\{\sqrt{3}\}-2\{\sqrt{2}\})$

How to solve $n^2-n<\lfloor\frac{n^2}{4}\rfloor$ ,$n \in \mathbb{N}$?

Prove $\int_0^n \lfloor x\rfloor \,dx = \frac{n (n-1)}{2}$

The number of real roots of $x\lfloor x\rfloor+187=\lfloor x^{2}\rfloor+\lfloor x\rfloor$

Equation involving floor function:

How to prove ceiling and floor inequality more 'formally'?

Possible circular reasoning in textbook proof that $\lceil x+m\rceil=\lceil x\rceil +m$

Conjectures Involving floor(x)/piecewise continuity with regards to Integration and Differential Equations

ceiling functions inequality

Compute $\lim_{x\to 0}\frac{x}{[x]}$

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