Question

For every $x\in\mathbb R$ and $\varepsilon$ > 0 , there exist $\,q,q'\in\mathbb Q$, such that $q<x<q'$ and $\left |q-q' \right |< \varepsilon$

score 222 · Answer 1 · 2014-09-24 14:32:29

222

Views

For every $x\in\mathbb R$ and $\varepsilon$ > 0 , there exist $\,q,q'\in\mathbb Q$, such that $q<x<q'$ and $\left |q-q' \right |< \varepsilon$

Published on 24 Sep 2014 - 14:32

score 386 · Answer 2 · 2014-09-25 01:46:33

386

Views

Proving that $x-\left\lfloor \frac{x}{2} \right\rfloor\; =\; \left\lfloor \frac{x+1}{2} \right\rfloor$

Published on 25 Sep 2014 - 1:46

score 1.3k · Answer 3 · 2026-03-25 21:45:54

1.3k

Views

Measurability of the floor function

Published on 25 Mar 2026 - 21:45

score 262 · Answer 4 · 2026-03-26 02:57:46

262

Views

Is it true that $\left\lfloor\sum_{s=1}^n\operatorname{Li}_s\left(\frac 1k \right)\right\rfloor\stackrel{?}{=}\left\lfloor\frac nk \right\rfloor$

Published on 26 Mar 2026 - 2:57

score 3.1k · Answer 5 · 2014-09-30 03:35:55

3.1k

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Finding the fourier series of floor function

Published on 30 Sep 2014 - 3:35

score 1.5k · Answer 6 · 2014-09-30 04:31:45

1.5k

Views

Inverse of a function containing the ceiling function over the natural numbers

Published on 30 Sep 2014 - 4:31

score 625 · Answer 7 · 2014-09-30 10:34:33

625

Views

A formula for $\lfloor n\rfloor+\left\lfloor \frac n2\right\rfloor+ \left\lfloor \frac n3\right\rfloor+\ldots+\left\lfloor \frac nk\right\rfloor$?

Published on 30 Sep 2014 - 10:34

score 167 · Answer 8 · 2014-09-30 13:43:18

167

Views

How prove this$\lfloor \sqrt{2x-\lfloor\sqrt{2x}\rfloor}\rfloor=\lfloor\frac{\sqrt{8x+1}-1}{2}\rfloor$

Published on 30 Sep 2014 - 13:43

score 92 · Answer 9 · 2026-03-25 21:48:47

92

Views

Determine $\left \{ u\geq a \right \}$ for all $a\in \mathbb{R}$, and is $u$ $\mathcal B(\mathbb{R})/\mathcal B(\mathbb{R})$-measurable?

Published on 25 Mar 2026 - 21:48

score 140 · Answer 10 · 2014-10-04 15:26:59

140

Views

How to calculate with $\lceil \cdot \rceil$

Published on 04 Oct 2014 - 15:26

score 71 · Answer 11 · 2014-10-04 18:17:46

71

Views

The solutions of the following equation

Published on 04 Oct 2014 - 18:17

score 71 · Answer 12 · 2014-10-07 14:40:59

71

Views

How to plot bivariate function involving modulus and floor functions?

Published on 07 Oct 2014 - 14:40

score 249 · Answer 13 · 2014-10-08 04:26:14

249

Views

$\lfloor x\rfloor + \lfloor y\rfloor \leq \lfloor x+y\rfloor$ for every pair of numbers of $x$ and $y$

Published on 08 Oct 2014 - 4:26

score 154 · Answer 14 · 2026-03-27 10:12:07

154

Views

Is there a simple closed form of $|\alpha(\sqrt{n}-\left\lfloor \sqrt{n} \right \rfloor) + \beta(\sqrt{n}-\left\lfloor \sqrt{n} \right \rfloor)|$?

Published on 27 Mar 2026 - 10:12

score 138 · Answer 15 · 2014-10-12 19:40:48

138

Views

Growth of $\sum_{x=1}^{n-1} \left\lceil n-\sqrt{n^{2}-x^{2} } \right\rceil$

Published on 12 Oct 2014 - 19:40

List Question

For every $x\in\mathbb R$ and $\varepsilon$ > 0 , there exist $\,q,q'\in\mathbb Q$, such that $q<x<q'$ and $\left |q-q' \right |< \varepsilon$

Proving that $x-\left\lfloor \frac{x}{2} \right\rfloor\; =\; \left\lfloor \frac{x+1}{2} \right\rfloor$

Measurability of the floor function

Is it true that $\left\lfloor\sum_{s=1}^n\operatorname{Li}_s\left(\frac 1k \right)\right\rfloor\stackrel{?}{=}\left\lfloor\frac nk \right\rfloor$

Finding the fourier series of floor function

Inverse of a function containing the ceiling function over the natural numbers

A formula for $\lfloor n\rfloor+\left\lfloor \frac n2\right\rfloor+ \left\lfloor \frac n3\right\rfloor+\ldots+\left\lfloor \frac nk\right\rfloor$?

How prove this$\lfloor \sqrt{2x-\lfloor\sqrt{2x}\rfloor}\rfloor=\lfloor\frac{\sqrt{8x+1}-1}{2}\rfloor$

Determine $\left \{ u\geq a \right \}$ for all $a\in \mathbb{R}$, and is $u$ $\mathcal B(\mathbb{R})/\mathcal B(\mathbb{R})$-measurable?

How to calculate with $\lceil \cdot \rceil$

The solutions of the following equation

How to plot bivariate function involving modulus and floor functions?

$\lfloor x\rfloor + \lfloor y\rfloor \leq \lfloor x+y\rfloor$ for every pair of numbers of $x$ and $y$

Is there a simple closed form of $|\alpha(\sqrt{n}-\left\lfloor \sqrt{n} \right \rfloor) + \beta(\sqrt{n}-\left\lfloor \sqrt{n} \right \rfloor)|$?

Growth of $\sum_{x=1}^{n-1} \left\lceil n-\sqrt{n^{2}-x^{2} } \right\rceil$

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