List questions from ceiling-and-floor-functions

Published on 06 Mar 2024 - 14:46

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Solve $\lfloor x-1\rfloor(3^x-2^x-\lfloor x^2\rfloor) = 0$

Published on 07 Mar 2024 - 10:38

18

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How to reduce division with uprounding to integer-arithmetic operations with downrounding if the denominator is not necessarily an integer?

Published on 27 Mar 2026 - 7:49

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integration of floor function

Published on 09 Mar 2024 - 15:24

29

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Solve recurrence $A(0)=0$, $A(n)=1+\min_{1\leq k\leq n}\left\{\max\left(\left\lfloor\frac{k-1}{2}\right\rfloor, A(n-k)\right)\right\}$.

Published on 11 Mar 2024 - 8:42

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Solving equation with two floor functions

Published on 16 Mar 2024 - 1:17

112

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Graphing $(\lfloor x \rfloor + \lfloor1-x\rfloor)$

Published on 26 Mar 2026 - 4:31

99

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$f(n)= \left\lfloor \frac{an+b}{cn+d} \right\rfloor , \forall n \in \mathbb N$ is surjective

Published on 20 Mar 2024 - 14:20

33

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Asymptotics of expression involving floor functions

Published on 24 Mar 2024 - 18:50

62

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For $0<x<1$, let $f(x)=\int_0^1\left( \left\lfloor\frac{x}{y}\right\rfloor-x \left\lfloor\frac{1}{y}\right\rfloor\right)dy\ldots$

Published on 24 Mar 2024 - 19:32

249

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Prove⌈a/b⌉ ≤ a/b + (b-1)/b

Published on 25 Mar 2024 - 5:34

147

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Prove that sum of integrals $= n$ for argument $n \in \mathbb{N}_{>1}$

Published on 25 Mar 2024 - 10:53

61

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How to compute the following limit? $\lim\limits_{x\to\ 0^+} {\frac{x-\lfloor x \rfloor}{x+\lfloor x \rfloor}}$

Published on 25 Mar 2026 - 23:13

58

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Computing $h(h(x))$ where $h (x) = \lfloor 5x - 2 \rfloor$

Published on 26 Mar 2024 - 13:32

31

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Sum of Floor Series

Published on 31 Mar 2024 - 9:23

List Question

Inverse of a piecewise floor function

Solve $\lfloor x-1\rfloor(3^x-2^x-\lfloor x^2\rfloor) = 0$

How to reduce division with uprounding to integer-arithmetic operations with downrounding if the denominator is not necessarily an integer?

integration of floor function

Solve recurrence $A(0)=0$, $A(n)=1+\min_{1\leq k\leq n}\left\{\max\left(\left\lfloor\frac{k-1}{2}\right\rfloor, A(n-k)\right)\right\}$.

Solving equation with two floor functions

Graphing $(\lfloor x \rfloor + \lfloor1-x\rfloor)$

$f(n)= \left\lfloor \frac{an+b}{cn+d} \right\rfloor , \forall n \in \mathbb N$ is surjective

Asymptotics of expression involving floor functions

For $0<x<1$, let $f(x)=\int_0^1\left( \left\lfloor\frac{x}{y}\right\rfloor-x \left\lfloor\frac{1}{y}\right\rfloor\right)dy\ldots$

Prove⌈a/b⌉ ≤ a/b + (b-1)/b

Prove that sum of integrals $= n$ for argument $n \in \mathbb{N}_{>1}$

How to compute the following limit? $\lim\limits_{x\to\ 0^+} {\frac{x-\lfloor x \rfloor}{x+\lfloor x \rfloor}}$

Computing $h(h(x))$ where $h (x) = \lfloor 5x - 2 \rfloor$

Sum of Floor Series

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