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fractional imaginary calculation

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#complex-numbers #matlab #fractional-part
99
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Prove $⌊2x⌋+⌊2y⌋≥⌊x⌋+⌊y⌋+⌊x+y⌋$

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#functions #ceiling-and-floor-functions #fractional-part
271
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Let $F_1$ and $F_2$ be the fractional parts of $(44-\sqrt 2017)^{2017}$ and $(44+ \sqrt 2017)^{2017}$ respectively. Then $F_1+F_2$ lies between?

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#fractional-part
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If matrix $A=[a_{ij}]_{4 \times 4}$ such that...

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#matrices #determinant #divisibility #fractional-part
54
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If $\{x\}:=x-\lfloor x\rfloor$, then are these the same? $\{l+m\}$, $\left\{l+\{m\}\right\}$, $\left\{\left\{l\right\}+\{m\}\right\}$

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#proof-verification #modular-arithmetic #fourier-analysis #signal-processing #fractional-part
146
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Is fractional part of $e^n$ dense in (0,1)?

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#real-analysis #fractional-part
136
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Prove that $\left|\left\{\frac{n}{1}\right\} - \left\{\frac{n}{2}\right\} - \cdots - (-1)^n\left\{\frac{n}{n}\right\}\right| \le \sqrt{2n}$.

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#inequality #fractional-part
184
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Evaluate the limit $\lim\limits_{n\to0}\frac{(x)+(2x)+\cdots (nx)}{n^2}$

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#real-analysis #limits #functions #sequence-of-function #fractional-part
49
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Find number of x such that $\{x\}+\{x^2\}=1,x\in(0,20). $Where $\{\}$ denotes fractional part.

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#fractional-part
67
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Relations between $\sqrt x$ and $\sqrt{x+n}$

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#arithmetic #fractional-part
4.2k
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Irrational fractional parts - patterns

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#irrational-numbers #fractional-part
83
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Verify my proof on elementary number theory

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#elementary-number-theory #proof-verification #divisibility #fractional-part
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limit involving sine of fractional part

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#limits #fractional-part
12.2k
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How to find out the period of fractional part of x

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#functions #periodic-functions #fractional-part
6k
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For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$

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#real-analysis #irrational-numbers #ceiling-and-floor-functions #fractional-part

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