Question

How do I prove that the $a^{b^{m}} \leftrightarrow b^{a^{n}}$ relations hold for any natural numbers $m, n$?

score 199 · Answer 1 · 2026-04-15 19:28:50

199

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How do I prove that the $a^{b^{m}} \leftrightarrow b^{a^{n}}$ relations hold for any natural numbers $m, n$?

Published on 15 Apr 2026 - 19:28

score 37 · Answer 2 · 2026-04-16 04:54:38

37

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Proving that the infinite self-composition of $f(x)= \frac{x}{2} + 1$ is 2 for any $x$ value

Published on 16 Apr 2026 - 4:54

score 283 · Answer 3 · 2026-04-14 19:51:30

283

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Proving that if $x+\frac{1}{x}$ is an integer, then $x^n+\frac{1}{x^n}$ is also an integer for all even $n$ using induction

Published on 14 Apr 2026 - 19:51

score 87 · Answer 4 · 2026-04-14 20:03:52

87

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How to prove $\int_0^\frac{\pi}{2} \sin^{r} \theta d \theta \int_0^\frac{\pi}{2} \sin^{r-1} \theta d \theta = \frac{\pi}{2r}$ without Beta properties?

Published on 14 Apr 2026 - 20:03

score 52 · Answer 5 · 2026-04-15 04:49:29

52

Views

Proving 2 related equations are the same

Published on 15 Apr 2026 - 4:49

score 228 · Answer 6 · 2026-04-15 21:12:03

228

Views

Prove that $\sum\limits_{cyc}\frac{a^2}{a^2+bc}+\frac{(a+b+c)^3+9abc}{\prod\limits_{cyc}(a+b)}\geq6.$

Published on 15 Apr 2026 - 21:12

score 573 · Answer 7 · 2026-04-14 05:31:51

573

Views

Proving that there always exists an n-degree polynomial passing through any $n+1$ points

Published on 14 Apr 2026 - 5:31

score 101 · Answer 8 · 2026-04-14 18:16:21

101

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Theorem 29.1 in Munkres' TOPOLOGY: A proposed simplification in the compactness part in Step 2 of the proof

Published on 14 Apr 2026 - 18:16

score 114 · Answer 9 · 2026-04-14 20:32:54

114

Views

Proving Group of Odd Order cannot be Doubly Transitive

Published on 14 Apr 2026 - 20:32

score 214 · Answer 10 · 2026-04-14 06:43:00

214

Views

Is there a proof that $\ 0<\alpha<1\implies\alpha^n\to\ 0\ $ without alluding to numbers greater than $\ 1,\ $ other than $n$ itself?

Published on 14 Apr 2026 - 6:43

score 202 · Answer 11 · 2026-04-12 15:25:36

202

Views

Simplifying $\frac{\tan A + \sec A - 1}{\tan A - \sec A + 1}$

Published on 12 Apr 2026 - 15:25

score 59 · Answer 12 · 2026-04-17 02:28:08

59

Views

$A - C = B-C$ iff $A \cup C = B \cup C$

Published on 17 Apr 2026 - 2:28

score 352 · Answer 13 · 2026-04-16 05:43:40

352

Views

Chapter 2 Exercise 2 Question (a) Page 84 Linda J. S. Allen 2010

Published on 16 Apr 2026 - 5:43

score 252 · Answer 14 · 2026-04-10 19:54:49

252

Views

Do polynomials have a limit ratio of 1 over fixed intervals?

Published on 10 Apr 2026 - 19:54

score 337 · Answer 15 · 2026-04-09 14:46:40

337

Views

What are some ways to show that $1$ is not first-order definable in $(\mathbb{R}, +, 0, \le)$?

Published on 09 Apr 2026 - 14:46

List Question

How do I prove that the $a^{b^{m}} \leftrightarrow b^{a^{n}}$ relations hold for any natural numbers $m, n$?

Proving that the infinite self-composition of $f(x)= \frac{x}{2} + 1$ is 2 for any $x$ value

Proving that if $x+\frac{1}{x}$ is an integer, then $x^n+\frac{1}{x^n}$ is also an integer for all even $n$ using induction

How to prove $\int_0^\frac{\pi}{2} \sin^{r} \theta d \theta \int_0^\frac{\pi}{2} \sin^{r-1} \theta d \theta = \frac{\pi}{2r}$ without Beta properties?

Proving 2 related equations are the same

Prove that $\sum\limits_{cyc}\frac{a^2}{a^2+bc}+\frac{(a+b+c)^3+9abc}{\prod\limits_{cyc}(a+b)}\geq6.$

Proving that there always exists an n-degree polynomial passing through any $n+1$ points

Theorem 29.1 in Munkres' TOPOLOGY: A proposed simplification in the compactness part in Step 2 of the proof

Proving Group of Odd Order cannot be Doubly Transitive

Is there a proof that $\ 0<\alpha<1\implies\alpha^n\to\ 0\ $ without alluding to numbers greater than $\ 1,\ $ other than $n$ itself?

Simplifying $\frac{\tan A + \sec A - 1}{\tan A - \sec A + 1}$

$A - C = B-C$ iff $A \cup C = B \cup C$

Chapter 2 Exercise 2 Question (a) Page 84 Linda J. S. Allen 2010

Do polynomials have a limit ratio of 1 over fixed intervals?

What are some ways to show that $1$ is not first-order definable in $(\mathbb{R}, +, 0, \le)$?

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