Question

Completing the proof using strong induction for $E = \bigcap_{n=1}^\infty E_n $

score 240 · Answer 1 · 2020-07-07 02:58:37

240

Views

Completing the proof using strong induction for $E = \bigcap_{n=1}^\infty E_n $

Published on 07 Jul 2020 - 2:58

score 152 · Answer 2 · 2020-07-07 10:37:08

152

Views

Is this proof valid to prove that $F(x)-G(x)$ is always non zero?

Published on 07 Jul 2020 - 10:37

score 60 · Answer 3 · 2026-03-25 17:38:35

60

Views

Proving that an inequality holds

Published on 25 Mar 2026 - 17:38

score 67 · Answer 4 · 2020-07-07 21:15:30

67

Views

Prove that $\sum_{j=0}^{\infty}z_{j}$ converges absolutely iff $\sum_{j=0}^{\infty}x_{j}$ and $\sum_{j=0}^{\infty}y_{j}$ converges absolutely

Published on 07 Jul 2020 - 21:15

score 136 · Answer 5 · 2026-03-28 15:59:38

136

Views

Use the arithmetic mean-geometric mean inequality to establish that $-x < n < m$ implies $(1+x/n)^{n} \leq (1 + x/m)^{m}$

Published on 28 Mar 2026 - 15:59

score 1.6k · Answer 6 · 2026-04-02 02:49:50

1.6k

Views

Intuition behind equation for volume of a cone without calculus

Published on 02 Apr 2026 - 2:49

score 104 · Answer 7 · 2026-02-23 12:09:13

104

Views

Show that a subset $I$ of $\textbf{R}$ is an interval if and only if whenever $a,b\in I$ and $0\leq t\leq 1$ then $(1-t)a + tb\in I$.

Published on 23 Feb 2026 - 12:09

score 70 · Answer 8 · 2026-03-31 08:11:16

70

Views

$A\subseteq\mathbb{R}$ is closed iff $\sup(A\cap[a,b])\in A$ and $\inf(A\cap[a,b])\in A$.

Published on 31 Mar 2026 - 8:11

score 571 · Answer 9 · 2020-07-09 19:49:44

571

Views

Another way to solve $\int \frac{\sin^4(x)}{1+\cos^2(x)}\ dx$ without the substitution $y=\tan\left(\frac{x}{2}\right)$?

Published on 09 Jul 2020 - 19:49

score 180 · Answer 10 · 2026-02-23 08:07:02

180

Views

Looking for an Alternative Proof of a Bound on the Number of Maximal Ideals in an Integral Extension Lying over a Maximal Ideal in the Base Ring

Published on 23 Feb 2026 - 8:07

score 71 · Answer 11 · 2020-07-10 20:28:39

71

Views

Prove the equivalence: $f$ is continuous on $A$ iff whenever $U$ is open in $\textbf{R}$, then $f^{-1}(U)$ is a relatively open subset of $A$.

Published on 10 Jul 2020 - 20:28

score 57 · Answer 12 · 2020-07-11 13:45:02

57

Views

Creating a proof and finding the real roots of unknown function

Published on 11 Jul 2020 - 13:45

score 64 · Answer 13 · 2020-07-11 22:04:32

64

Views

Help to solve $y'=y$, building exp function

Published on 11 Jul 2020 - 22:04

score 319 · Answer 14 · 2020-07-12 05:52:17

319

Views

Any finite connected graph with every vertex has degree $\ge 2$ has a circuit

Published on 12 Jul 2020 - 5:52

score 72 · Answer 15 · 2020-07-12 23:30:33

72

Views

if $\frac{p}{q}, \frac{r}{s}$ are positive simplified fractions such that $qr - ps=1$, prove that $\frac{p+r}{q+s}$ is also a simplified fraction

Published on 12 Jul 2020 - 23:30

List Question

Completing the proof using strong induction for $E = \bigcap_{n=1}^\infty E_n $

Is this proof valid to prove that $F(x)-G(x)$ is always non zero?

Proving that an inequality holds

Prove that $\sum_{j=0}^{\infty}z_{j}$ converges absolutely iff $\sum_{j=0}^{\infty}x_{j}$ and $\sum_{j=0}^{\infty}y_{j}$ converges absolutely

Use the arithmetic mean-geometric mean inequality to establish that $-x < n < m$ implies $(1+x/n)^{n} \leq (1 + x/m)^{m}$

Intuition behind equation for volume of a cone without calculus

Show that a subset $I$ of $\textbf{R}$ is an interval if and only if whenever $a,b\in I$ and $0\leq t\leq 1$ then $(1-t)a + tb\in I$.

$A\subseteq\mathbb{R}$ is closed iff $\sup(A\cap[a,b])\in A$ and $\inf(A\cap[a,b])\in A$.

Another way to solve $\int \frac{\sin^4(x)}{1+\cos^2(x)}\ dx$ without the substitution $y=\tan\left(\frac{x}{2}\right)$?

Looking for an Alternative Proof of a Bound on the Number of Maximal Ideals in an Integral Extension Lying over a Maximal Ideal in the Base Ring

Prove the equivalence: $f$ is continuous on $A$ iff whenever $U$ is open in $\textbf{R}$, then $f^{-1}(U)$ is a relatively open subset of $A$.

Creating a proof and finding the real roots of unknown function

Help to solve $y'=y$, building exp function

Any finite connected graph with every vertex has degree $\ge 2$ has a circuit

if $\frac{p}{q}, \frac{r}{s}$ are positive simplified fractions such that $qr - ps=1$, prove that $\frac{p+r}{q+s}$ is also a simplified fraction

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