List questions from irrationality-measure

Published on 06 Feb 2021 - 14:08

203

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Roth's theorem: contradiction?

Published on 26 Feb 2021 - 9:58

222

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Approximation of a random number with quadratic integers

Published on 05 Mar 2021 - 22:40

133

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Measuring Irrationality à la 3Blue1Brown vs Liouville

Published on 20 Mar 2021 - 9:15

371

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Are Rational Power of e is transcendental?

Published on 23 Mar 2021 - 5:54

116

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Decimal expansions of $0.999\cdot\cdot$ and $1.000\cdot \cdot$ (infinite digits)

Published on 24 Oct 2021 - 19:43

113

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Why is irrationality mesure of irrational numbers at least 2

Published on 18 Nov 2021 - 18:54

137

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Let $a_1$ be linearly independent to $a_2$ over $\mathbb{Q}.$ For $n\geq 3,$ let $ a_n = \vert a_{n-1} - a_{n-2} \vert.$ Does $\sum_n a_n\ $ converge?

Published on 13 Jun 2022 - 14:56

135

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Understanding Liouville numbers and irrationality measure

Published on 05 Aug 2022 - 10:42

39

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Showing that linear fractional equivalences preserve the irrationality measure

Published on 17 Aug 2022 - 21:46

72

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Why does $|x-p/q|\ge\frac{C(x)}{q^a}$ for all $p/q$ imply: "$|x-p/q|\lt\frac{1}{q^a}$ has only finitely many solutions"?

Published on 18 Aug 2022 - 12:45

90

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Given $\alpha\in \mathbb{R},$ do there exist arbitrarily large $m,k$ such that $\vert \alpha - \frac{k}{m}\vert < \frac{1}{m^2}$?

Published on 02 Oct 2022 - 19:06

55

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If $x,y>1,$ does there exist $\varepsilon>0,\ N,M\in\mathbb{N}$ s.t. $\lvert x^n-y^m\rvert>\varepsilon\quad\forall n\geq N,\quad \forall\ m\geq M?$

Published on 16 Nov 2022 - 22:11

List Question

About irrationality measure.

Roth's theorem: contradiction?

Approximation of a random number with quadratic integers

Measuring Irrationality à la 3Blue1Brown vs Liouville

Are Rational Power of e is transcendental?

Decimal expansions of $0.999\cdot\cdot$ and $1.000\cdot \cdot$ (infinite digits)

Why is irrationality mesure of irrational numbers at least 2

Let $a_1$ be linearly independent to $a_2$ over $\mathbb{Q}.$ For $n\geq 3,$ let $ a_n = \vert a_{n-1} - a_{n-2} \vert.$ Does $\sum_n a_n\ $ converge?

Understanding Liouville numbers and irrationality measure

Showing that linear fractional equivalences preserve the irrationality measure

Why does $|x-p/q|\ge\frac{C(x)}{q^a}$ for all $p/q$ imply: "$|x-p/q|\lt\frac{1}{q^a}$ has only finitely many solutions"?

Given $\alpha\in \mathbb{R},$ do there exist arbitrarily large $m,k$ such that $\vert \alpha - \frac{k}{m}\vert < \frac{1}{m^2}$?

If $x,y>1,$ does there exist $\varepsilon>0,\ N,M\in\mathbb{N}$ s.t. $\lvert x^n-y^m\rvert>\varepsilon\quad\forall n\geq N,\quad \forall\ m\geq M?$

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