Question

Show that the number of multiples of $m$ in $[1, x]$ is $\lfloor \frac{x}{m} \rfloor$

score 73 · Answer 1 · 2018-08-03 14:42:29

73

Views

Show that the number of multiples of $m$ in $[1, x]$ is $\lfloor \frac{x}{m} \rfloor$

Published on 03 Aug 2018 - 14:42

score 574 · Answer 2 · 2018-08-09 13:02:45

574

Views

Given the equation $\sum_{k=11}^{99} \left[x + \frac{k}{100} \right] = 765$ find $[10 \, x]$.

Published on 09 Aug 2018 - 13:02

score 288 · Answer 3 · 2018-08-09 16:58:49

288

Views

Signed harmonic series containing floor function

Published on 09 Aug 2018 - 16:58

score 120 · Answer 4 · 2018-08-10 15:54:45

120

Views

Convergence of stochastic process divided by floor.

Published on 10 Aug 2018 - 15:54

score 1.1k · Answer 5 · 2018-08-11 15:49:42

1.1k

Views

Inverse floor function

Published on 11 Aug 2018 - 15:49

score 64 · Answer 6 · 2018-08-14 00:20:05

64

Views

prove that $x∉ℤ⇒\lfloor{-x}\rfloor=-\lfloor{x}\rfloor-1$

Published on 14 Aug 2018 - 0:20

score 265 · Answer 7 · 2018-08-14 16:40:56

265

Views

Prove that, $\left\lfloor{\frac{x}{n}}\right\rfloor=\left\lfloor{\frac{\lfloor{x}\rfloor}{n}}\right\rfloor$ where $n \in{\mathbb{N}}$

Published on 14 Aug 2018 - 16:40

score 58 · Answer 8 · 2018-08-14 18:59:58

58

Views

Prove that $\lfloor{x}\rfloor=\bigg\lfloor{\frac{x+1}{2}}\bigg\rfloor+\bigg\lfloor{\frac{x+2}{2^2}}\bigg\rfloor+\ldots$

Published on 14 Aug 2018 - 18:59

score 55 · Answer 9 · 2018-08-15 08:48:14

55

Views

Why isn't this true for $x<0$?

Published on 15 Aug 2018 - 8:48

score 939 · Answer 10 · 2018-08-16 19:27:25

939

Views

For any prime number $p$, let $A_p$ be the set of integers $d\in \{1,2,\dots, 999\}$ s. Then what is the cardinality of $A_p$?

Published on 16 Aug 2018 - 19:27

score 147 · Answer 11 · 2018-08-18 02:58:38

147

Views

Prove $\forall x,y \in \mathbb{R} :\lfloor{x+y}\rfloor=\lfloor{x}\rfloor+\lfloor{y}\rfloor∨\lfloor{x+y}\rfloor=\lfloor{x}\rfloor+\lfloor{y}\rfloor+1$

Published on 18 Aug 2018 - 2:58

score 68 · Answer 12 · 2018-08-20 14:45:44

68

Views

Find the cardinality of the set $A_p$ defined as the following :

Published on 20 Aug 2018 - 14:45

score 123 · Answer 13 · 2026-03-25 07:43:14

123

Views

Properties of floors, ceilings and modulus

Published on 25 Mar 2026 - 7:43

score 78 · Answer 14 · 2026-03-25 06:12:13

78

Views

Solve for $x$ in the equation containing ${\lfloor{x}\rfloor}$ and $\{x\}$

Published on 25 Mar 2026 - 6:12

score 314 · Answer 15 · 2018-08-29 15:16:12

314

Views

The priority of limits

Published on 29 Aug 2018 - 15:16

List Question

Show that the number of multiples of $m$ in $[1, x]$ is $\lfloor \frac{x}{m} \rfloor$

Given the equation $\sum_{k=11}^{99} \left[x + \frac{k}{100} \right] = 765$ find $[10 \, x]$.

Signed harmonic series containing floor function

Convergence of stochastic process divided by floor.

Inverse floor function

prove that $x∉ℤ⇒\lfloor{-x}\rfloor=-\lfloor{x}\rfloor-1$

Prove that, $\left\lfloor{\frac{x}{n}}\right\rfloor=\left\lfloor{\frac{\lfloor{x}\rfloor}{n}}\right\rfloor$ where $n \in{\mathbb{N}}$

Prove that $\lfloor{x}\rfloor=\bigg\lfloor{\frac{x+1}{2}}\bigg\rfloor+\bigg\lfloor{\frac{x+2}{2^2}}\bigg\rfloor+\ldots$

Why isn't this true for $x<0$?

For any prime number $p$, let $A_p$ be the set of integers $d\in \{1,2,\dots, 999\}$ s. Then what is the cardinality of $A_p$?

Prove $\forall x,y \in \mathbb{R} :\lfloor{x+y}\rfloor=\lfloor{x}\rfloor+\lfloor{y}\rfloor∨\lfloor{x+y}\rfloor=\lfloor{x}\rfloor+\lfloor{y}\rfloor+1$

Find the cardinality of the set $A_p$ defined as the following :

Properties of floors, ceilings and modulus

Solve for $x$ in the equation containing ${\lfloor{x}\rfloor}$ and $\{x\}$

The priority of limits

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