Question

Is $\frac{2 \cdot 4\cdot 8 \cdot 16 \cdots}{1\cdot 3\cdot 7\cdot15 \cdots}$ irrational?

score 184 · Answer 1 · 2022-02-09 14:08:22

184

Views

Is $\frac{2 \cdot 4\cdot 8 \cdot 16 \cdots}{1\cdot 3\cdot 7\cdot15 \cdots}$ irrational?

Published on 09 Feb 2022 - 14:08

score 51 · Answer 2 · 2022-03-27 11:34:48

51

Views

If $a=b+c$ , $a^2$ is an integer, can $b^2$ or $c^2$ or both be irrational?

Published on 27 Mar 2022 - 11:34

score 59 · Answer 3 · 2022-04-14 05:34:51

59

Views

If $\log_3(A)$ is rational, can $\log_3(A+1)$ be rational? (Where $A$ is a positive real number.)

Published on 14 Apr 2022 - 5:34

score 204 · Answer 4 · 2022-05-04 13:55:58

204

Views

Prove that when the denominator of a rational number is of the form $2^n * 5^m$ it is a terminating decimal

Published on 04 May 2022 - 13:55

score 261 · Answer 5 · 2022-05-26 17:16:13

261

Views

What are some techniques to prove that a set of numbers is rationally independent?

Published on 26 May 2022 - 17:16

score 55 · Answer 6 · 2022-09-17 09:05:53

55

Views

Regarding the rationality of $T_k = x^k + \frac{1}{x^k}$, given $T_m$ and $T_n$ are rational for some $m,n \in \mathbb{N}$.

Published on 17 Sep 2022 - 9:05

score 63 · Answer 7 · 2022-10-16 08:32:55

63

Views

Does the maximum entropy Nash equilibrium with integer payoffs have rational probabilities?

Published on 16 Oct 2022 - 8:32

score 76 · Answer 8 · 2022-11-10 22:54:35

76

Views

Directions for a proof of the irrationality of $\pi$ from Archimedes' approximation

Published on 10 Nov 2022 - 22:54

score 99 · Answer 9 · 2022-11-13 08:41:55

99

Views

Prove that number $\sqrt{2}$ is an irrational number using this theorem "if $a^2$ is even, $a$ must be even"

Published on 13 Nov 2022 - 8:41

score 88 · Answer 10 · 2026-02-23 17:26:27

88

Views

Prove $\sqrt{2}+\sqrt{3}+\sqrt{5}+...+\sqrt{p_{n}}$ is irrational, where $p_{n}$ is the nth prime.

Published on 23 Feb 2026 - 17:26

score 275 · Answer 11 · 2023-01-16 10:29:29

275

Views

$ֿ\sqrt{2}$ is irrational. Proof by contradiction or Proof of Negation?

Published on 16 Jan 2023 - 10:29

List Question

Is $\frac{2 \cdot 4\cdot 8 \cdot 16 \cdots}{1\cdot 3\cdot 7\cdot15 \cdots}$ irrational?

If $a=b+c$ , $a^2$ is an integer, can $b^2$ or $c^2$ or both be irrational?

If $\log_3(A)$ is rational, can $\log_3(A+1)$ be rational? (Where $A$ is a positive real number.)

Prove that when the denominator of a rational number is of the form $2^n * 5^m$ it is a terminating decimal

What are some techniques to prove that a set of numbers is rationally independent?

Regarding the rationality of $T_k = x^k + \frac{1}{x^k}$, given $T_m$ and $T_n$ are rational for some $m,n \in \mathbb{N}$.

Does the maximum entropy Nash equilibrium with integer payoffs have rational probabilities?

Directions for a proof of the irrationality of $\pi$ from Archimedes' approximation

Prove that number $\sqrt{2}$ is an irrational number using this theorem "if $a^2$ is even, $a$ must be even"

Prove $\sqrt{2}+\sqrt{3}+\sqrt{5}+...+\sqrt{p_{n}}$ is irrational, where $p_{n}$ is the nth prime.

$ֿ\sqrt{2}$ is irrational. Proof by contradiction or Proof of Negation?

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