List questions from ceiling-and-floor-functions

Published on 30 Mar 2026 - 2:06

359

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Maximum Value of a Floor-y Function

Published on 10 Aug 2015 - 18:19

97

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Can this expression: $\left \lfloor \left(\frac x 2 \right)^2\right \rfloor $ be rewritten without the floor part?

Published on 12 Aug 2015 - 21:58

216

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Then the value of $ [f(2)] $ where [.] represents the greatest integer function is?

Published on 13 Aug 2015 - 13:32

134

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Find the limit $\lim_{ n\rightarrow \infty} \frac{\left\lfloor\frac{3n}{10}\right\rfloor}{n}$

Published on 16 Aug 2015 - 13:31

102

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Why does $\lfloor x \rfloor \leq n \iff x < n+1$ but $\lfloor x\rfloor < n \iff x< n$?

Published on 16 Aug 2015 - 17:59

270

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Solving Equations Containing Floor Functions

Published on 16 Aug 2015 - 23:40

1k

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How to prove this identity of ceiling function?

Published on 17 Aug 2015 - 14:14

144

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For any arithmetic progression $n \in \Bbb{N} : n \equiv b \pmod a$, the natural density is $\frac{1}{a}$?

Published on 28 Mar 2026 - 23:59

765

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Composing Even and Odd Functions With Floors

Published on 29 Mar 2026 - 2:45

2.7k

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The floor function's relationship with odd and even functions

Published on 22 Aug 2015 - 13:08

108

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How to pigeonhole the primes between $p_n$ and $p_{n+1}^2$ for twin prime conjecture?

Published on 25 Mar 2026 - 20:35

222

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$\left[\frac n1\right]+ \left[\frac n2\right] + \cdots+\left[\frac nn\right]+\left[\sqrt n\right]$ is even

Published on 26 Mar 2026 - 8:00

194

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Floor and Ceiling Series (I)

Published on 01 Sep 2015 - 17:51

756

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Integrating Floor Functions

Published on 05 Sep 2015 - 4:28

List Question

$\lfloor x^k \rfloor \equiv m \pmod{n}$ with $x$ irrational

Maximum Value of a Floor-y Function

Can this expression: $\left \lfloor \left(\frac x 2 \right)^2\right \rfloor $ be rewritten without the floor part?

Then the value of $ [f(2)] $ where [.] represents the greatest integer function is?

Find the limit $\lim_{ n\rightarrow \infty} \frac{\left\lfloor\frac{3n}{10}\right\rfloor}{n}$

Why does $\lfloor x \rfloor \leq n \iff x < n+1$ but $\lfloor x\rfloor < n \iff x< n$?

Solving Equations Containing Floor Functions

How to prove this identity of ceiling function?

For any arithmetic progression $n \in \Bbb{N} : n \equiv b \pmod a$, the natural density is $\frac{1}{a}$?

Composing Even and Odd Functions With Floors

The floor function's relationship with odd and even functions

How to pigeonhole the primes between $p_n$ and $p_{n+1}^2$ for twin prime conjecture?

$\left[\frac n1\right]+ \left[\frac n2\right] + \cdots+\left[\frac nn\right]+\left[\sqrt n\right]$ is even

Floor and Ceiling Series (I)

Integrating Floor Functions

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