Question

Show $f(x) = x - \lfloor x \rfloor$ is bounded in $[0,2]$, but has no maximum in $[0,2]$.

score 50 · Answer 1 · 2020-05-24 09:00:32

50

Views

Show $f(x) = x - \lfloor x \rfloor$ is bounded in $[0,2]$, but has no maximum in $[0,2]$.

Published on 24 May 2020 - 9:00

score 263 · Answer 2 · 2020-05-26 01:15:10

263

Views

How do I prove the floor identity $⌊x + n⌋ = ⌊x⌋ + n$ in a more precise way?

Published on 26 May 2020 - 1:15

score 128 · Answer 3 · 2020-05-27 03:50:45

128

Views

A functional equation involving the floor function.

Published on 27 May 2020 - 3:50

score 60 · Answer 4 · 2026-03-27 15:58:59

60

Views

Floor equation with square roots

Published on 27 Mar 2026 - 15:58

score 35 · Answer 5 · 2020-05-30 09:40:58

35

Views

Solving a system of equations involving the floor function.

Published on 30 May 2020 - 9:40

score 84 · Answer 6 · 2020-05-31 01:14:32

84

Views

Which of the following is true about $f(x)=\int_0^x[t]dt$?

Published on 31 May 2020 - 1:14

score 64 · Answer 7 · 2020-05-31 13:01:57

64

Views

How to simplify this summation involving floor functions?

Published on 31 May 2020 - 13:01

score 42 · Answer 8 · 2020-06-02 23:52:41

42

Views

Conversion of a system of equations containing floor function to a single function

Published on 02 Jun 2020 - 23:52

score 83 · Answer 9 · 2020-06-05 10:04:36

83

Views

Proving $f(x,n)=\lfloor x \lfloor x \lfloor x \lfloor x ...(\text{n times})\rfloor\rfloor \rfloor \rfloor $ is increasing for $x>0$

Published on 05 Jun 2020 - 10:04

score 55 · Answer 10 · 2020-06-06 09:44:03

55

Views

Find number of $n\in\{1,2,\dotsc,1000\}$ s.t. $\exists x\in\mathbb{R}^+$ where $x^2+\lfloor x^2\rfloor=n$.

Published on 06 Jun 2020 - 9:44

score 647 · Answer 11 · 2020-06-06 16:27:19

647

Views

Modulo operation with floor function

Published on 06 Jun 2020 - 16:27

score 240 · Answer 12 · 2026-03-25 15:52:33

240

Views

Solving $f(f(f(x))) = 17$ when $f(x)=x\{x\}$

Published on 25 Mar 2026 - 15:52

score 116 · Answer 13 · 2020-06-07 01:23:23

116

Views

Simplify $\sum_{k = 0}^{[p/3] - 2} \sum_{i = 1}^{[p/(k + 1)] - 3} \sum_{j = 0}^{p - (k + 1) (i + 2) - 1} {\delta}_{N, i\, p + j + k + 1}$

Published on 07 Jun 2020 - 1:23

score 297 · Answer 14 · 2020-06-09 14:42:43

297

Views

Prove that $\lceil \log_{10}(n) \rceil$ equals the number of digits of $n \ne 10^a$

Published on 09 Jun 2020 - 14:42

score 1.1k · Answer 15 · 2020-06-10 13:15:59

1.1k

Views

Floor function of a product

Published on 10 Jun 2020 - 13:15

List Question

Show $f(x) = x - \lfloor x \rfloor$ is bounded in $[0,2]$, but has no maximum in $[0,2]$.

How do I prove the floor identity $⌊x + n⌋ = ⌊x⌋ + n$ in a more precise way?

A functional equation involving the floor function.

Floor equation with square roots

Solving a system of equations involving the floor function.

Which of the following is true about $f(x)=\int_0^x[t]dt$?

How to simplify this summation involving floor functions?

Conversion of a system of equations containing floor function to a single function

Proving $f(x,n)=\lfloor x \lfloor x \lfloor x \lfloor x ...(\text{n times})\rfloor\rfloor \rfloor \rfloor $ is increasing for $x>0$

Find number of $n\in\{1,2,\dotsc,1000\}$ s.t. $\exists x\in\mathbb{R}^+$ where $x^2+\lfloor x^2\rfloor=n$.

Modulo operation with floor function

Solving $f(f(f(x))) = 17$ when $f(x)=x\{x\}$

Simplify $\sum_{k = 0}^{[p/3] - 2} \sum_{i = 1}^{[p/(k + 1)] - 3} \sum_{j = 0}^{p - (k + 1) (i + 2) - 1} {\delta}_{N, i\, p + j + k + 1}$

Prove that $\lceil \log_{10}(n) \rceil$ equals the number of digits of $n \ne 10^a$

Floor function of a product

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