List questions from irrational-numbers

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Understanding proof that $\pi$ is irrational

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How would you prove that $\sqrt[n]{2}$ is irrational?

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Irrationality of e and farey fractions

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Help with a proof that sequence of rational numbers $ a_n = \frac {a_{n-1} + \frac {2}{a_{n-1}}}{2}$ converges to an irrational, $\sqrt2$

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Irrationality Measure $x\in \mathbb{Q} \Longleftrightarrow \mu(x)=1$

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Help with a proof my professor gave my class

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Help proving a theorem in my textbook

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If $(a_n)$ is increasing and $\lim_{n\to\infty}\frac{a_{n+1}}{a_1\dotsb a_n}=+\infty$ then $\sum\limits_{n=1}^\infty\frac1{a_n}$ is irrational

Published on 15 Apr 2026 - 8:12

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Is $\sum\limits_{n=1}^\infty\frac1{a_n}$ irrational?

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Do circles exist

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If $\sum\frac1{a_n}$ is convergent, then irrational?

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Is Dirichlet's function enough to prove constants like $\gamma$ irrational?

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List Question

Check that $\sqrt{7}(\sqrt[3]{5} - \sqrt[5]{3})$ is not rational

Farey sequence problem with irrational numbers

Understanding proof that $\pi$ is irrational

How would you prove that $\sqrt[n]{2}$ is irrational?

Irrationality of e and farey fractions

Help with a proof that sequence of rational numbers $ a_n = \frac {a_{n-1} + \frac {2}{a_{n-1}}}{2}$ converges to an irrational, $\sqrt2$

Irrationality Measure $x\in \mathbb{Q} \Longleftrightarrow \mu(x)=1$

Irrationality of $\pi$ another proof

Help with a proof my professor gave my class

Help proving a theorem in my textbook

If $(a_n)$ is increasing and $\lim_{n\to\infty}\frac{a_{n+1}}{a_1\dotsb a_n}=+\infty$ then $\sum\limits_{n=1}^\infty\frac1{a_n}$ is irrational

Is $\sum\limits_{n=1}^\infty\frac1{a_n}$ irrational?

Do circles exist

If $\sum\frac1{a_n}$ is convergent, then irrational?

Is Dirichlet's function enough to prove constants like $\gamma$ irrational?

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