Question

My question is whether given function is periodic or not

score 51 · Answer 1 · 2026-04-01 03:39:36

51

Views

My question is whether given function is periodic or not

Published on 01 Apr 2026 - 3:39

score 148 · Answer 2 · 2024-02-24 04:10:37

148

Views

Can this proof that $\sqrt{2}$ is irrational be rewritten using only integers?

Published on 24 Feb 2024 - 4:10

score 128 · Answer 3 · 2024-03-02 15:35:30

128

Views

Why must rational $x$ and $y$ satisfy $x+y=2$ and $2\sqrt{3xy}=3$ in order for $2\sqrt{3}-3=(x+y)\sqrt{3}-2\sqrt{3xy}$ to be true?

Published on 02 Mar 2024 - 15:35

score 108 · Answer 4 · 2026-03-29 09:11:34

108

Views

Does there exist an irrational number $x$ such that both $x^π$ and $π^x$ are also irrational?

Published on 29 Mar 2026 - 9:11

score 65 · Answer 5 · 2024-03-09 21:28:02

65

Views

How to prove the constant's power x series?

Published on 09 Mar 2024 - 21:28

score 105 · Answer 6 · 2024-03-10 15:56:45

105

Views

Question about an inequality during proof that $e^2$ is irrational.

Published on 10 Mar 2024 - 15:56

score 95 · Answer 7 · 2024-03-14 17:22:38

95

Views

Prove that $\sqrt{18} - \sqrt{12}-\sqrt{45} + \sqrt{6}$ is irrational

Published on 14 Mar 2024 - 17:22

score 36 · Answer 8 · 2024-03-15 04:20:20

36

Views

Let $a_n\geq a>0$, for any $x\in\Bbb R$, can we find a rational sequence $r_n$ such that $r_na_n\to x$?

Published on 15 Mar 2024 - 4:20

score 105 · Answer 9 · 2026-03-25 13:58:01

105

Views

Might there be an $n^{\text{th}}$ digit of $\pi$ where the sequence becomes palindromic?

Published on 25 Mar 2026 - 13:58

score 163 · Answer 10 · 2024-03-29 07:51:55

163

Views

Prove that $r+x$ is irrational.

Published on 29 Mar 2024 - 7:51

score 1.5k · Answer 11 · 2026-03-29 09:11:27

1.5k

Views

$e^{\pi\sqrt N}$ is very close to an integer for some smallish $N$s. What about $\pi^{e\sqrt N}$?

Published on 29 Mar 2026 - 9:11

score 926 · Answer 12 · 2015-01-11 23:11:19

926

Views

What do we mean when we say an irrational number can't be expressed as a fraction?

Published on 11 Jan 2015 - 23:11

score 64 · Answer 13 · 2026-03-31 23:32:27

64

Views

Can we deduce that $⌊r^{n}α⌋≃r^{n}α$ when $r→∞$?

Published on 31 Mar 2026 - 23:32

score 110 · Answer 14 · 2015-01-25 22:39:23

110

Views

"Multivariable" version of this lemma about showing analytically that a number is irrational.

Published on 25 Jan 2015 - 22:39

score 4k · Answer 15 · 2026-03-26 11:18:20

4k

Views

Prove that the quotient of a nonzero rational number and an irrational number is irrational

Published on 26 Mar 2026 - 11:18

List Question

My question is whether given function is periodic or not

Can this proof that $\sqrt{2}$ is irrational be rewritten using only integers?

Why must rational $x$ and $y$ satisfy $x+y=2$ and $2\sqrt{3xy}=3$ in order for $2\sqrt{3}-3=(x+y)\sqrt{3}-2\sqrt{3xy}$ to be true?

Does there exist an irrational number $x$ such that both $x^π$ and $π^x$ are also irrational?

How to prove the constant's power x series?

Question about an inequality during proof that $e^2$ is irrational.

Prove that $\sqrt{18} - \sqrt{12}-\sqrt{45} + \sqrt{6}$ is irrational

Let $a_n\geq a>0$, for any $x\in\Bbb R$, can we find a rational sequence $r_n$ such that $r_na_n\to x$?

Might there be an $n^{\text{th}}$ digit of $\pi$ where the sequence becomes palindromic?

Prove that $r+x$ is irrational.

$e^{\pi\sqrt N}$ is very close to an integer for some smallish $N$s. What about $\pi^{e\sqrt N}$?

What do we mean when we say an irrational number can't be expressed as a fraction?

Can we deduce that $⌊r^{n}α⌋≃r^{n}α$ when $r→∞$?

"Multivariable" version of this lemma about showing analytically that a number is irrational.

Prove that the quotient of a nonzero rational number and an irrational number is irrational

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