List questions from irrational-numbers

Published on 23 Mar 2026 - 12:35

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$\alpha$ is an irrational number. Is $\liminf_{n\rightarrow\infty}n\{ n\alpha\}$ always positive?

Published on 17 Mar 2026 - 13:24

136

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Is this : $\sqrt{3+\sqrt{2+\sqrt{3+\sqrt{2+\sqrt{\cdots}}}}}$ irrational number?

Published on 17 Mar 2026 - 14:05

170

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ls $\sqrt{2}+\sqrt{3}$ the only sum of two irrational which close to $\pi$?

Published on 26 Mar 2026 - 13:57

64

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Find an equation where all 'y' is always irrational for all integer values of x

Published on 17 Mar 2026 - 8:26

99

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Is a irrational number still irrational when we apply some mapping to its decimal representation?

Published on 17 Mar 2026 - 10:35

67

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Density of a real subset $A$ such that $\forall (a,b) \in A^2, \ \sqrt{ab} \in A$

Published on 24 Mar 2026 - 15:38

62

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Proof of irrationality

Published on 26 Mar 2026 - 21:35

380

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Is there an essential difference between Cartwright's and Niven's proofs of the irrationality of $\pi$?

Published on 26 Mar 2026 - 17:13

135

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Where am I making a mistake in showing that countability isn't a thing?

Published on 17 Mar 2026 - 3:32

102

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Ambiguity in Question!

Published on 26 Mar 2026 - 19:28

5.4k

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Is this a valid proof? If $a$ and $b$ are rational, $a^b$ is rational.

Published on 22 Mar 2026 - 4:09

99

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Real solution of equations of 2018

Published on 27 Mar 2026 - 1:33

140

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Is the real number whose $n^{\rm th}$ digit after the decimal point in decimal representation is the leading digit of $2^n$ a rational number?

Published on 20 Mar 2026 - 4:32

52

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Nested fractional denominator(up to infinity)calculation

Published on 25 Mar 2026 - 7:58

List Question

Convergence of a rational sequence to a irrational limit

$\alpha$ is an irrational number. Is $\liminf_{n\rightarrow\infty}n\{ n\alpha\}$ always positive?

Is this : $\sqrt{3+\sqrt{2+\sqrt{3+\sqrt{2+\sqrt{\cdots}}}}}$ irrational number?

ls $\sqrt{2}+\sqrt{3}$ the only sum of two irrational which close to $\pi$?

Find an equation where all 'y' is always irrational for all integer values of x

Is a irrational number still irrational when we apply some mapping to its decimal representation?

Density of a real subset $A$ such that $\forall (a,b) \in A^2, \ \sqrt{ab} \in A$

Proof of irrationality

Is there an essential difference between Cartwright's and Niven's proofs of the irrationality of $\pi$?

Where am I making a mistake in showing that countability isn't a thing?

Ambiguity in Question!

Is this a valid proof? If $a$ and $b$ are rational, $a^b$ is rational.

Real solution of equations of 2018

Is the real number whose $n^{\rm th}$ digit after the decimal point in decimal representation is the leading digit of $2^n$ a rational number?

Nested fractional denominator(up to infinity)calculation

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