Question

How do I prove that the floor function has no limit?

score 212 · Answer 1 · 2016-02-07 20:20:27

212

Views

How do I prove that the floor function has no limit?

Published on 07 Feb 2016 - 20:20

score 89 · Answer 2 · 2016-02-07 20:57:27

89

Views

Proof that $\lfloor x + x\sqrt3 \rfloor = x + \lfloor x\sqrt3 \rfloor$ Where $x \in N$

Published on 07 Feb 2016 - 20:57

score 1.2k · Answer 3 · 2016-02-08 12:45:36

1.2k

Views

Find the limit $\lim_{n\to\infty}\left(\sqrt{n^2+n+1}-\left\lfloor\sqrt{n^2+n+1}\right\rfloor\right)$

Published on 08 Feb 2016 - 12:45

score 94 · Answer 4 · 2016-02-09 20:49:39

94

Views

Is this identity about floor function true?

Published on 09 Feb 2016 - 20:49

score 135 · Answer 5 · 2016-02-10 04:51:07

135

Views

How do I deal with a floor function is a system of equations?

Published on 10 Feb 2016 - 4:51

score 318 · Answer 6 · 2016-02-10 15:59:12

318

Views

Solve the equation $7t+[2t] =52 $ ,where $[x]$ denotes the floor function for $x$.

Published on 10 Feb 2016 - 15:59

score 133 · Answer 7 · 2016-02-11 19:01:53

133

Views

Find all real $x$ such that $1990[x] +1989[-x]=1$ (where $[x]$ is the floor function for $x$).

Published on 11 Feb 2016 - 19:01

score 69 · Answer 8 · 2016-02-14 12:40:49

69

Views

Find another closed form for this sequence

Published on 14 Feb 2016 - 12:40

score 249 · Answer 9 · 2016-02-15 08:33:55

249

Views

sum of floor ("weighted" divisor summary function)

Published on 15 Feb 2016 - 8:33

score 47 · Answer 10 · 2016-02-15 14:13:36

47

Views

Round to down - Remainder emulation?

Published on 15 Feb 2016 - 14:13

score 273 · Answer 11 · 2016-02-15 20:34:01

273

Views

Proving that $\lceil x-\lceil y \rceil \rceil =\lfloor \lceil x \rceil - y \rfloor$

Published on 15 Feb 2016 - 20:34

score 5.8k · Answer 12 · 2016-02-16 17:08:55

5.8k

Views

Inequalities with floor function

Published on 16 Feb 2016 - 17:08

score 632 · Answer 13 · 2016-02-17 01:43:57

632

Views

For all $x$ which are real numbers, prove that $\lfloor 2x\rfloor = \lfloor x\rfloor + \lfloor x+0.5\rfloor.$

Published on 17 Feb 2016 - 1:43

score 54 · Answer 14 · 2016-02-18 09:29:20

54

Views

Showing that percentage of the coefficients of $(x+y)^n$ being even tends towards $100\%$ when taking the limit of $n$ to infinity

Published on 18 Feb 2016 - 9:29

score 327 · Answer 15 · 2026-03-26 09:18:08

327

Views

Proving $\lim_{n\to\infty}\sum_{k=n}^{\infty}\Big(\frac{1}{n\left\lfloor\frac kn\right\rfloor}-\frac1k\Big)=\gamma$

Published on 26 Mar 2026 - 9:18

List Question

How do I prove that the floor function has no limit?

Proof that $\lfloor x + x\sqrt3 \rfloor = x + \lfloor x\sqrt3 \rfloor$ Where $x \in N$

Find the limit $\lim_{n\to\infty}\left(\sqrt{n^2+n+1}-\left\lfloor\sqrt{n^2+n+1}\right\rfloor\right)$

Is this identity about floor function true?

How do I deal with a floor function is a system of equations?

Solve the equation $7t+[2t] =52 $ ,where $[x]$ denotes the floor function for $x$.

Find all real $x$ such that $1990[x] +1989[-x]=1$ (where $[x]$ is the floor function for $x$).

Find another closed form for this sequence

sum of floor ("weighted" divisor summary function)

Round to down - Remainder emulation?

Proving that $\lceil x-\lceil y \rceil \rceil =\lfloor \lceil x \rceil - y \rfloor$

Inequalities with floor function

For all $x$ which are real numbers, prove that $\lfloor 2x\rfloor = \lfloor x\rfloor + \lfloor x+0.5\rfloor.$

Showing that percentage of the coefficients of $(x+y)^n$ being even tends towards $100\%$ when taking the limit of $n$ to infinity

Proving $\lim_{n\to\infty}\sum_{k=n}^{\infty}\Big(\frac{1}{n\left\lfloor\frac kn\right\rfloor}-\frac1k\Big)=\gamma$

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