List questions from fractional-part

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What is the closest fraction (that isn't something like 31415.../1000...) that gets you pretty close to pi?

Published on 12 Jan 2025 - 23:36

63

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For $n\in\mathbb{N}$, evaluate $\int_0^n \cos(2\pi \lfloor x\rfloor\{x\})dx$

Published on 12 Jan 2025 - 9:15

173

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What is a field with bounded whole and unbounded fractional part called?

Published on 12 Jan 2025 - 23:37

120

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Find $\lim_{x\to 0^{\pm}}f(x)=\frac{\arcsin(1-\left\{x\right\})\times\arccos(1-\left\{x\right\})}{\sqrt{2\left\{x\right\}}\times(1-\left\{x\right\})}$

Published on 12 Jan 2025 - 9:26

245

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fractional chromatic number

Published on 12 Jan 2025 - 18:07

193

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Summation of fractional parts $\frac{m}{n}$, where $2 \leq n < m$ (amateur)

Published on 12 Jan 2025 - 9:25

1.1k

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Prove that limit of the fractional part of $\sqrt{n^2+n}$ is $\frac{1}{2}$

Published on 12 Jan 2025 - 9:26

61

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Simplifiying (or getting the exponent thing outside) the expression $\{({\rm complicated\, stuff})^{1/n}\}$

Published on 12 Jan 2025 - 9:25

83

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If $l>10$ and $\{a\}>\frac{1}{l}$ then there exists $k \in \{1,\dots, l\}$ such that $\{ka\} \in [1/10,2/10]$

Published on 12 Jan 2025 - 9:26

2.5k

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If $x$, $\{x\}$, $\lfloor x\rfloor$ are in G.P, find $x$.

Published on 12 Jan 2025 - 9:25

List Question

What is the closest fraction (that isn't something like 31415.../1000...) that gets you pretty close to pi?

For $n\in\mathbb{N}$, evaluate $\int_0^n \cos(2\pi \lfloor x\rfloor\{x\})dx$

What is a field with bounded whole and unbounded fractional part called?

Find $\lim_{x\to 0^{\pm}}f(x)=\frac{\arcsin(1-\left\{x\right\})\times\arccos(1-\left\{x\right\})}{\sqrt{2\left\{x\right\}}\times(1-\left\{x\right\})}$

fractional chromatic number

Summation of fractional parts $\frac{m}{n}$, where $2 \leq n < m$ (amateur)

Prove that limit of the fractional part of $\sqrt{n^2+n}$ is $\frac{1}{2}$

Simplifiying (or getting the exponent thing outside) the expression $\{({\rm complicated\, stuff})^{1/n}\}$

If $l>10$ and $\{a\}>\frac{1}{l}$ then there exists $k \in \{1,\dots, l\}$ such that $\{ka\} \in [1/10,2/10]$

If $x$, $\{x\}$, $\lfloor x\rfloor$ are in G.P, find $x$.

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