Question

Property of greatest integer function

score 1.5k · Answer 1 · 2014-10-14 20:13:29

1.5k

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Property of greatest integer function

Published on 14 Oct 2014 - 20:13

score 358 · Answer 2 · 2014-10-15 23:22:05

358

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Closed form solution for $\left \lfloor{\frac{a}{x}}\right \rfloor$ = $\left \lfloor{\frac{b}{x}}\right \rfloor$?

Published on 15 Oct 2014 - 23:22

score 757 · Answer 3 · 2014-10-16 14:30:32

757

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Show that $\, 0 \leq \left \lfloor{\frac{2a}{b}}\right \rfloor - 2 \left \lfloor{\frac{a}{b}}\right \rfloor \leq 1 $

Published on 16 Oct 2014 - 14:30

score 81 · Answer 4 · 2014-10-16 16:02:09

81

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Is $\frac{1}{\lfloor \frac{a}{b} \rfloor}=\lceil \frac{b}{a} \rceil$??

Published on 16 Oct 2014 - 16:02

score 243 · Answer 5 · 2014-10-16 17:52:07

Prove that for all positive integers $x$, $\left\lfloor \frac{x^2 +2x + 2}{4}\right\rfloor =\left\lfloor \frac{x^2 + 2x + 1}{4}\right\rfloor$.

score 3.8k · Answer 6 · 2014-10-19 23:50:53

3.8k

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Limit of floor function when $x$ goes infinity

Published on 19 Oct 2014 - 23:50

score 594 · Answer 7 · 2026-03-25 15:38:56

594

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Zeroes of the floor (greatest integer function)

Published on 25 Mar 2026 - 15:38

score 58 · Answer 8 · 2014-10-29 16:18:04

58

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How should I approach solving this floor function?

Published on 29 Oct 2014 - 16:18

score 307 · Answer 9 · 2014-10-29 16:24:16

307

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floor ceiling proof

Published on 29 Oct 2014 - 16:24

score 75 · Answer 10 · 2014-10-31 07:35:21

75

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If $x>y$, then $\lfloor x\rfloor\ge \lfloor y\rfloor$, formal proof

Published on 31 Oct 2014 - 7:35

score 75 · Answer 11 · 2014-10-31 15:11:10

75

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Is this statement false? if so, how should I disprove it?

Published on 31 Oct 2014 - 15:11

score 205 · Answer 12 · 2026-03-25 12:28:14

205

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Calculation of value of $ \int_{0}^{n}\cos\left(\lfloor x \rfloor\cdot \{x\}\right)dx\;,$

Published on 25 Mar 2026 - 12:28

score 355 · Answer 13 · 2014-11-03 23:02:02

355

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Finding the limit when there is the mantissa function involved

Published on 03 Nov 2014 - 23:02

score 391 · Answer 14 · 2014-11-11 12:59:36

391

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$x = c + (\lfloor \frac{y}{m} \rfloor \times m) - y$ resulting in negative number

Published on 11 Nov 2014 - 12:59

score 2.1k · Answer 15 · 2014-11-13 23:39:22

2.1k

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Proving that $ \lfloor \lceil x \rceil \rfloor = \lceil x \rceil $ for all real numbers $ x $.

Published on 13 Nov 2014 - 23:39

List Question

Property of greatest integer function

Closed form solution for $\left \lfloor{\frac{a}{x}}\right \rfloor$ = $\left \lfloor{\frac{b}{x}}\right \rfloor$?

Show that $\, 0 \leq \left \lfloor{\frac{2a}{b}}\right \rfloor - 2 \left \lfloor{\frac{a}{b}}\right \rfloor \leq 1 $

Is $\frac{1}{\lfloor \frac{a}{b} \rfloor}=\lceil \frac{b}{a} \rceil$??

Prove that for all positive integers $x$, $\left\lfloor \frac{x^2 +2x + 2}{4}\right\rfloor =\left\lfloor \frac{x^2 + 2x + 1}{4}\right\rfloor$.

Limit of floor function when $x$ goes infinity

Zeroes of the floor (greatest integer function)

How should I approach solving this floor function?

floor ceiling proof

If $x>y$, then $\lfloor x\rfloor\ge \lfloor y\rfloor$, formal proof

Is this statement false? if so, how should I disprove it?

Calculation of value of $ \int_{0}^{n}\cos\left(\lfloor x \rfloor\cdot \{x\}\right)dx\;,$

Finding the limit when there is the mantissa function involved

$x = c + (\lfloor \frac{y}{m} \rfloor \times m) - y$ resulting in negative number

Proving that $ \lfloor \lceil x \rceil \rfloor = \lceil x \rceil $ for all real numbers $ x $.

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