Question

If $a$ is algebraic over $F$ and $b$ is transcendental over $F$, then $a+b$ is transcendental over $F$.

score 1.1k · Answer 1 · 2026-03-22 02:19:30

1.1k

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If $a$ is algebraic over $F$ and $b$ is transcendental over $F$, then $a+b$ is transcendental over $F$.

Published on 22 Mar 2026 - 2:19

score 34 · Answer 2 · 2026-03-22 10:17:43

34

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Proof for $-4\pi^2+48\ne A+B\pi+C\pi^2$ when $(A,B,C)\ne (48,0,-4)$

Published on 22 Mar 2026 - 10:17

score 356 · Answer 3 · 2026-03-22 14:55:19

356

Views

Different types of transcendental numbers based on continued-fraction representation

Published on 22 Mar 2026 - 14:55

score 570 · Answer 4 · 2026-03-21 16:22:16

570

Views

Smallest Subset of $\mathbb{R}_{>0}$ Closed under Typical Operations

Published on 21 Mar 2026 - 16:22

score 180 · Answer 5 · 2026-03-21 23:50:58

180

Views

Extending the set of algebraic numbers

Published on 21 Mar 2026 - 23:50

score 665 · Answer 6 · 2026-03-21 12:29:08

665

Views

Transcendental a infinitely close to rationals?

Published on 21 Mar 2026 - 12:29

score 570 · Answer 7 · 2026-03-22 02:22:54

570

Views

Is $\pi$ a rational multiple of e?

Published on 22 Mar 2026 - 2:22

score 201 · Answer 8 · 2019-10-13 22:14:42

201

Views

relation between rational and irrational, non-transcendental numbers?

Published on 13 Oct 2019 - 22:14

score 140 · Answer 9 · 2019-10-20 19:03:13

140

Views

Is There a "Geometric" Way to Calculate Transcendental Numbers (Monte Carlo Method but for other numbers)?

Published on 20 Oct 2019 - 19:03

score 57 · Answer 10 · 2019-10-25 08:19:32

57

Views

How is continued fraction of numbers like pi are calculated

Published on 25 Oct 2019 - 8:19

score 78 · Answer 11 · 2019-10-26 02:33:12

78

Views

Is $e^e$ equal to every point on the circle $z=|e^e|$?

Published on 26 Oct 2019 - 2:33

score 165 · Answer 12 · 2019-10-29 21:26:04

165

Views

‘Square the circle’ by rotating and enlarging inscribed square toward circumscribed

Published on 29 Oct 2019 - 21:26

score 76 · Answer 13 · 2019-10-31 16:42:42

76

Views

Explanation for $\pi^3\approx \frac{3650e+999}{1000}+e^3$

Published on 31 Oct 2019 - 16:42

score 36 · Answer 14 · 2019-11-04 11:20:33

Numbers that are not roots of equations involving linear combinations with integer coefficients of compositions of monomials and certain functions

score 202 · Answer 15 · 2019-11-05 03:08:58

202

Views

Is there a simple proof that $\cos(1)$ is transcendental?

Published on 05 Nov 2019 - 3:08

List Question

If $a$ is algebraic over $F$ and $b$ is transcendental over $F$, then $a+b$ is transcendental over $F$.

Proof for $-4\pi^2+48\ne A+B\pi+C\pi^2$ when $(A,B,C)\ne (48,0,-4)$

Different types of transcendental numbers based on continued-fraction representation

Smallest Subset of $\mathbb{R}_{>0}$ Closed under Typical Operations

Extending the set of algebraic numbers

Transcendental a infinitely close to rationals?

Is $\pi$ a rational multiple of e?

relation between rational and irrational, non-transcendental numbers?

Is There a "Geometric" Way to Calculate Transcendental Numbers (Monte Carlo Method but for other numbers)?

How is continued fraction of numbers like pi are calculated

Is $e^e$ equal to every point on the circle $z=|e^e|$?

‘Square the circle’ by rotating and enlarging inscribed square toward circumscribed

Explanation for $\pi^3\approx \frac{3650e+999}{1000}+e^3$

Numbers that are not roots of equations involving linear combinations with integer coefficients of compositions of monomials and certain functions

Is there a simple proof that $\cos(1)$ is transcendental?

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