List questions from irrational-numbers

Published on 26 Mar 2026 - 18:59

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Are numbers like $\left ( -2 \right )^{\sqrt{2}}$ real or complex?

Published on 29 Mar 2026 - 14:57

2.1k

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Irrational number "test"?

Published on 15 Aug 2014 - 15:20

482

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$1$ is not congruent because of Fermat's Last Theorem?

Published on 18 Aug 2014 - 23:56

14k

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For an irrational number $a$ the fractional part of $na$ for $n\in\mathbb N$ is dense in $[0,1]$

Published on 19 Aug 2014 - 16:04

34

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Existence of a sequence of integers $\lbrace a_k\rbrace_{k\geq 1}$ so that the first $k$ digits of $a_k\alpha$ are $0$ where $\alpha$ is irrational.

Published on 19 Aug 2014 - 16:26

315

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How do you multiply infinite quantities?

Published on 29 Mar 2026 - 3:20

167

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Rational values of $\sin(\log(x))$

Published on 29 Mar 2026 - 20:49

2.7k

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Is $\ln\sqrt{2}$ irrational?

Published on 25 Aug 2014 - 12:20

146

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How is circle closed?

Published on 26 Aug 2014 - 11:35

166

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If $q^n$ is irrational for all $n>1$, then $q$ is irrational.

Published on 29 Mar 2026 - 12:05

1k

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What are some examples of proofs using the Pythagorean assumption that all segments are commensurable?

Published on 30 Mar 2026 - 3:37

458

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Can one prove existence of incommensurables without the Pythagorean theorem?

Published on 29 Mar 2026 - 8:44

1.1k

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Process to show that $\sqrt 2+\sqrt[3] 3$ is irrational

Published on 30 Aug 2014 - 14:08

283

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Correctness of the proof that the set $\{x \in \mathbb{Q} : x>0 \text{ and } x^2>2\}$ does not have a smallest element

Published on 29 Mar 2026 - 20:51

List Question

Lambert's Original Proof that $\pi$ is irrational.

Are numbers like $\left ( -2 \right )^{\sqrt{2}}$ real or complex?

Irrational number "test"?

$1$ is not congruent because of Fermat's Last Theorem?

For an irrational number $a$ the fractional part of $na$ for $n\in\mathbb N$ is dense in $[0,1]$

Existence of a sequence of integers $\lbrace a_k\rbrace_{k\geq 1}$ so that the first $k$ digits of $a_k\alpha$ are $0$ where $\alpha$ is irrational.

How do you multiply infinite quantities?

Rational values of $\sin(\log(x))$

Is $\ln\sqrt{2}$ irrational?

How is circle closed?

If $q^n$ is irrational for all $n>1$, then $q$ is irrational.

What are some examples of proofs using the Pythagorean assumption that all segments are commensurable?

Can one prove existence of incommensurables without the Pythagorean theorem?

Process to show that $\sqrt 2+\sqrt[3] 3$ is irrational

Correctness of the proof that the set $\{x \in \mathbb{Q} : x>0 \text{ and } x^2>2\}$ does not have a smallest element

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