Question

prove that if x is a real number, then $\lfloor2x\rfloor=\lfloor x\rfloor+\lfloor x + \frac{1}{2}\rfloor$

score 8.2k · Answer 1 · 2016-10-22 04:51:44

8.2k

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prove that if x is a real number, then $\lfloor2x\rfloor=\lfloor x\rfloor+\lfloor x + \frac{1}{2}\rfloor$

Published on 22 Oct 2016 - 4:51

score 151 · Answer 2 · 2016-10-22 09:35:54

151

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How do I prove that $[\frac{x}{n}]+[\frac{x+1}{n}]+[\frac{x+2}{n}]....+[\frac{x+n-1}{n}]=[x]$

Published on 22 Oct 2016 - 9:35

score 379 · Answer 3 · 2016-10-23 21:07:04

379

Views

Floor function sum identity

Published on 23 Oct 2016 - 21:07

score 924 · Answer 4 · 2016-10-25 04:48:56

924

Views

Floor and ceiling Functions Equal?

Published on 25 Oct 2016 - 4:48

score 35 · Answer 5 · 2026-03-27 15:19:04

35

Views

Can we show that $\frac1{2^n}\lceil2^nx\rceil\downarrow x$ for $n\to\infty$?

Published on 27 Mar 2026 - 15:19

score 323 · Answer 6 · 2016-10-28 07:44:02

323

Views

Floor function values of $x$

Published on 28 Oct 2016 - 7:44

score 1.2k · Answer 7 · 2016-10-28 18:45:30

1.2k

Views

Inequalities on greatest integer function

Published on 28 Oct 2016 - 18:45

score 211 · Answer 8 · 2026-03-25 17:21:40

211

Views

How to evaluate $ \int_0^n \cos(2\pi \lfloor x\rfloor\{x\})dx$?

Published on 25 Mar 2026 - 17:21

score 193 · Answer 9 · 2016-10-28 21:33:33

193

Views

Exponential floor function inequalities

Published on 28 Oct 2016 - 21:33

score 41 · Answer 10 · 2016-10-31 05:20:30

41

Views

Why the two distribution are the same

Published on 31 Oct 2016 - 5:20

score 10.8k · Answer 11 · 2016-11-01 21:00:34

10.8k

Views

How do I prove that the ceiling of the floor of x is equal to the floor of x?

Published on 01 Nov 2016 - 21:00

score 4.2k · Answer 12 · 2016-11-01 21:34:03

4.2k

Views

Prove or disprove the the floor of xy is equal to the floor of x times the floor of y for all real numbers x and y.

Published on 01 Nov 2016 - 21:34

score 461 · Answer 13 · 2016-11-05 12:25:01

461

Views

Find the limit with floor sequence or prove that it doesn't exist

Published on 05 Nov 2016 - 12:25

score 59 · Answer 14 · 2016-11-06 14:15:09

59

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$\{\lfloor na\rfloor\mid n\in\mathbb N\}\cup\{\lfloor nb\rfloor\mid n\in\mathbb N\}$ is a permutation of $\mathbb N$ iff $ab=a+b$

Published on 06 Nov 2016 - 14:15

score 38 · Answer 15 · 2026-03-28 14:05:22

38

Views

How to compute$\lfloor k^{\frac{m}{n}}\rfloor$?

Published on 28 Mar 2026 - 14:05

List Question

prove that if x is a real number, then $\lfloor2x\rfloor=\lfloor x\rfloor+\lfloor x + \frac{1}{2}\rfloor$

How do I prove that $[\frac{x}{n}]+[\frac{x+1}{n}]+[\frac{x+2}{n}]....+[\frac{x+n-1}{n}]=[x]$

Floor function sum identity

Floor and ceiling Functions Equal?

Can we show that $\frac1{2^n}\lceil2^nx\rceil\downarrow x$ for $n\to\infty$?

Floor function values of $x$

Inequalities on greatest integer function

How to evaluate $ \int_0^n \cos(2\pi \lfloor x\rfloor\{x\})dx$?

Exponential floor function inequalities

Why the two distribution are the same

How do I prove that the ceiling of the floor of x is equal to the floor of x?

Prove or disprove the the floor of xy is equal to the floor of x times the floor of y for all real numbers x and y.

Find the limit with floor sequence or prove that it doesn't exist

$\{\lfloor na\rfloor\mid n\in\mathbb N\}\cup\{\lfloor nb\rfloor\mid n\in\mathbb N\}$ is a permutation of $\mathbb N$ iff $ab=a+b$

How to compute$\lfloor k^{\frac{m}{n}}\rfloor$?

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