Question

Find all non-negative real numbers $a_1$ $\le$ $a_2$ $\le$ $\ldots$ $\le$ $a_n$

score 83 · Answer 1 · 2026-04-14 14:34:05

83

Views

Find all non-negative real numbers $a_1$ $\le$ $a_2$ $\le$ $\ldots$ $\le$ $a_n$

Published on 14 Apr 2026 - 14:34

score 1.5k · Answer 2 · 2026-05-10 16:29:34

1.5k

Views

Proving piecewise function is not continuous

Published on 10 May 2026 - 16:29

score 131 · Answer 3 · 2026-04-16 16:18:26

131

Views

Proving $1 +\sqrt[3]{5-\sqrt2}$ is rational via the rational roots theorem

Published on 16 Apr 2026 - 16:18

score 94 · Answer 4 · 2026-05-10 13:50:18

94

Views

Prove that $\sqrt[3]p+\sqrt[3]{p^5}$ is irrational if $p$ is prime

Published on 10 May 2026 - 13:50

score 69 · Answer 5 · 2026-05-10 18:27:49

69

Views

How does Siegel's Lemma and properties of auxiliary functions helps in transcendental/irrationality proofs?

Published on 10 May 2026 - 18:27

score 321 · Answer 6 · 2026-05-14 06:36:18

321

Views

If $x^2$ and $x^3$ are rational, does it imply that $x$ is rational?

Published on 14 May 2026 - 6:36

score 193 · Answer 7 · 2026-04-16 05:31:04

193

Views

If $x$ and $y$ are irrational, then $x^y$ is irrational

Published on 16 Apr 2026 - 5:31

score 127 · Answer 8 · 2026-04-15 01:14:45

127

Views

Show that $\sqrt{abc}$ is irrational if $a, b, c$, and $\sqrt{a} + \sqrt{b} + \sqrt{c}$ are irrational.

Published on 15 Apr 2026 - 1:14

score 30 · Answer 9 · 2026-04-10 17:58:15

30

Views

Are the roots of polynomials "with almost integer" roots irrational?

Published on 10 Apr 2026 - 17:58

score 150 · Answer 10 · 2026-04-12 08:01:46

150

Views

When does a polynomial with integer coefficients have only irrational roots?

Published on 12 Apr 2026 - 8:01

score 76 · Answer 11 · 2026-04-14 08:55:40

76

Views

Prove ${e}^{x}$, $x\in\mathbb{Z}$ is irrational

Published on 14 Apr 2026 - 8:55

score 693 · Answer 12 · 2026-04-17 08:49:45

693

Views

Approximating $\frac {\log(5/4)}{\log(3/2)}$ to a rational number

Published on 17 Apr 2026 - 8:49

score 115 · Answer 13 · 2026-04-16 05:08:25

115

Views

$n ^{\rm th}$ digit of an irrational number

Published on 16 Apr 2026 - 5:08

score 52 · Answer 14 · 2026-04-15 10:18:06

52

Views

Is ok to differentiate and integrate when trying to prove that a number $x=p/q$ is irrational?

Published on 15 Apr 2026 - 10:18

score 165 · Answer 15 · 2026-04-15 12:16:54

165

Views

Cauchy sequences of rationals with limit irrational: natural, or geometric examples

Published on 15 Apr 2026 - 12:16

List Question

Find all non-negative real numbers $a_1$ $\le$ $a_2$ $\le$ $\ldots$ $\le$ $a_n$

Proving piecewise function is not continuous

Proving $1 +\sqrt[3]{5-\sqrt2}$ is rational via the rational roots theorem

Prove that $\sqrt[3]p+\sqrt[3]{p^5}$ is irrational if $p$ is prime

How does Siegel's Lemma and properties of auxiliary functions helps in transcendental/irrationality proofs?

If $x^2$ and $x^3$ are rational, does it imply that $x$ is rational?

If $x$ and $y$ are irrational, then $x^y$ is irrational

Show that $\sqrt{abc}$ is irrational if $a, b, c$, and $\sqrt{a} + \sqrt{b} + \sqrt{c}$ are irrational.

Are the roots of polynomials "with almost integer" roots irrational?

When does a polynomial with integer coefficients have only irrational roots?

Prove ${e}^{x}$, $x\in\mathbb{Z}$ is irrational

Approximating $\frac {\log(5/4)}{\log(3/2)}$ to a rational number

$n ^{\rm th}$ digit of an irrational number

Is ok to differentiate and integrate when trying to prove that a number $x=p/q$ is irrational?

Cauchy sequences of rationals with limit irrational: natural, or geometric examples

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