Question

Validity of "circular" proofs

score 177 · Answer 1 · 2014-05-30 11:02:10

177

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Validity of "circular" proofs

Published on 30 May 2014 - 11:02

score 11.5k · Answer 2 · 2014-05-31 17:06:09

11.5k

Views

$e^{i\theta}$ $=$ $\cos \theta + i \sin \theta$, a definition or theorem?

Published on 31 May 2014 - 17:06

score 4.2k · Answer 3 · 2014-06-03 23:14:26

4.2k

Views

Prove that the dual graph of any (planar) graph is connected

Published on 03 Jun 2014 - 23:14

score 849 · Answer 4 · 2014-06-04 18:22:59

849

Views

Seeking a more direct proof for: $m+n\mid f(m)+f(n)\implies m-n\mid f(m)-f(n)$

Published on 04 Jun 2014 - 18:22

score 156 · Answer 5 · 2014-06-05 19:18:39

156

Views

Orbit-Stabiliser Theorem Application

Published on 05 Jun 2014 - 19:18

score 291 · Answer 6 · 2026-03-29 10:15:26

291

Views

inequality $\prod\limits_{k=1}^n\frac{2k-1}{2k}\lt\frac1{\sqrt{3n}}$

Published on 29 Mar 2026 - 10:15

score 357 · Answer 7 · 2014-06-08 18:36:35

357

Views

Left & right adjoints in the context of complete lattices.

Published on 08 Jun 2014 - 18:36

score 2.4k · Answer 8 · 2014-06-09 00:45:24

2.4k

Views

Convergence of Alternating harmonic series (Direct!)

Published on 09 Jun 2014 - 0:45

score 5.3k · Answer 9 · 2014-06-10 14:55:51

5.3k

Views

Prove that n!+1 contains a prime factor greater than n and use this to prove that there are infinte many primes

Published on 10 Jun 2014 - 14:55

score 218 · Answer 10 · 2026-03-25 18:50:37

218

Views

Prove that $\dfrac{\sigma_1(n)}{n} = \sigma_{-1}(n)$ where $\sigma_x(n)$ is the sum of the $x$th powers of the positive divisors of $n$.

Published on 25 Mar 2026 - 18:50

score 807 · Answer 11 · 2014-06-13 22:02:56

807

Views

Alternative Proof of Infinitely Many Primes?

Published on 13 Jun 2014 - 22:02

score 1.6k · Answer 12 · 2014-06-14 14:31:58

1.6k

Views

Area of the intersection of two discs: Integral solution?

Published on 14 Jun 2014 - 14:31

score 98 · Answer 13 · 2014-06-15 22:49:03

98

Views

Give alternative proof of given theorem (relates to inverses of functions) need to use (b,a)∈ $B\times A.$

Published on 15 Jun 2014 - 22:49

score 87 · Answer 14 · 2014-06-16 14:27:54

87

Views

Help complete proof ('or' statement in conclusion): $a^2 \ge 7a \Rightarrow a\le0 \text { or } a\ge7$

Published on 16 Jun 2014 - 14:27

score 29 · Answer 15 · 2014-06-17 21:35:56

29

Views

Is this alternate answer right?

Published on 17 Jun 2014 - 21:35

List Question

Validity of "circular" proofs

$e^{i\theta}$ $=$ $\cos \theta + i \sin \theta$, a definition or theorem?

Prove that the dual graph of any (planar) graph is connected

Seeking a more direct proof for: $m+n\mid f(m)+f(n)\implies m-n\mid f(m)-f(n)$

Orbit-Stabiliser Theorem Application

inequality $\prod\limits_{k=1}^n\frac{2k-1}{2k}\lt\frac1{\sqrt{3n}}$

Left & right adjoints in the context of complete lattices.

Convergence of Alternating harmonic series (Direct!)

Prove that n!+1 contains a prime factor greater than n and use this to prove that there are infinte many primes

Prove that $\dfrac{\sigma_1(n)}{n} = \sigma_{-1}(n)$ where $\sigma_x(n)$ is the sum of the $x$th powers of the positive divisors of $n$.

Alternative Proof of Infinitely Many Primes?

Area of the intersection of two discs: Integral solution?

Give alternative proof of given theorem (relates to inverses of functions) need to use (b,a)∈ $B\times A.$

Help complete proof ('or' statement in conclusion): $a^2 \ge 7a \Rightarrow a\le0 \text { or } a\ge7$

Is this alternate answer right?

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