List questions from ceiling-and-floor-functions

Published on 31 Oct 2023 - 20:56

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Determine the points of continuity of $h(x)=\lfloor \sin(x) \rfloor$.

Published on 31 Oct 2023 - 22:39

138

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Floor function equations

Published on 01 Nov 2023 - 21:24

134

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Solution Verification Solve the equation $\frac{38-11x}{6}=\{\frac{2x+1}{6}\}+\{\frac{x+17}{3}\}$ in the set of real numbers

Published on 25 Mar 2026 - 21:54

113

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Need a function to identify co-prime pairs

Published on 05 Nov 2023 - 20:12

48

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Prove that for any real number $x, \sum_{i=1}^n a_i \lfloor ix \rfloor\ge 0$

Published on 07 Nov 2023 - 20:16

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Prove that $\int_0^1\lfloor nx\rfloor^2 dx = \frac{1}{n}\sum_{k=1}^{n-1} k^2$

Published on 08 Nov 2023 - 15:41

46

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Formula for the $N$th term of a recurrence relation involving greatest integer function

Published on 12 Nov 2023 - 5:16

86

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Area enclosed by $[|x|].[|y|]=2$, where $[.]$ is the greatest integer function

Published on 13 Nov 2023 - 6:11

131

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Find the solutions of $3\{x\} = 2x + [x]$ where $\{.\}$ denotes the fractional part and $[.]$ denotes the greatest integer function.

Published on 15 Nov 2023 - 13:55

50

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Simple question on limits and ceiling function

Published on 16 Nov 2023 - 21:21

65

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Question If my argument needs proof

Published on 21 Nov 2023 - 21:38

51

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Why $ \ \lfloor\sqrt n\rfloor= j(2j+1)$

Published on 22 Nov 2023 - 23:34

30

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Determine possible values of a floor function

Published on 23 Nov 2023 - 13:38

55

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closed-form expression for solution of inequality $ \left\lceil \frac{a}{x} \right\rceil > b$

Published on 26 Nov 2023 - 1:14

List Question

Proving an inequality involving floor division of positive integers?

Determine the points of continuity of $h(x)=\lfloor \sin(x) \rfloor$.

Floor function equations

Solution Verification Solve the equation $\frac{38-11x}{6}=\{\frac{2x+1}{6}\}+\{\frac{x+17}{3}\}$ in the set of real numbers

Need a function to identify co-prime pairs

Prove that for any real number $x, \sum_{i=1}^n a_i \lfloor ix \rfloor\ge 0$

Prove that $\int_0^1\lfloor nx\rfloor^2 dx = \frac{1}{n}\sum_{k=1}^{n-1} k^2$

Formula for the $N$th term of a recurrence relation involving greatest integer function

Area enclosed by $[|x|].[|y|]=2$, where $[.]$ is the greatest integer function

Find the solutions of $3\{x\} = 2x + [x]$ where $\{.\}$ denotes the fractional part and $[.]$ denotes the greatest integer function.

Simple question on limits and ceiling function

Question If my argument needs proof

Why $ \ \lfloor\sqrt n\rfloor= j(2j+1)$

Determine possible values of a floor function

closed-form expression for solution of inequality $ \left\lceil \frac{a}{x} \right\rceil > b$

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