Question

Prove the Positive Orthant is Open (Proof Verification)

score 327 · Answer 1 · 2020-04-15 23:03:55

327

Views

Prove the Positive Orthant is Open (Proof Verification)

Published on 15 Apr 2020 - 23:03

score 116 · Answer 2 · 2026-03-30 07:09:24

116

Views

Proof verification: Let $a_{n}$ be a sequence of real numbers bounded by $M\in\textbf{R}$, and which is also increasing. Then $a_{n}$ is convergent.

Published on 30 Mar 2026 - 7:09

score 161 · Answer 3 · 2020-04-16 01:38:42

161

Views

Is $\displaystyle \sum_{k = 1}^n\frac{1}{k^2} \leq 2 -\frac{1}{n}$ correctly proved by induction?

Published on 16 Apr 2020 - 1:38

score 73 · Answer 4 · 2020-04-16 02:52:47

73

Views

Suppose the sequences $a_{n}$ and $b_{n}$ converge to $a$ and $b$, respectively. Then the sequence $(a_{n}b_{n})_{n=m}^{\infty}$ converges to $ab$.

Published on 16 Apr 2020 - 2:52

score 39 · Answer 5 · 2026-04-02 22:25:52

39

Views

A problem on nowhere dense sets in metric spaces.

Published on 02 Apr 2026 - 22:25

score 1.5k · Answer 6 · 2020-04-16 05:14:19

1.5k

Views

Show that there is a $c\in(0,1)$ such that $f(c)=\int_0^cf(x)dx$.

Published on 16 Apr 2020 - 5:14

score 25 · Answer 7 · 2020-04-16 08:52:22

25

Views

Let $f(x) = \frac{1-x}{1+x}$ and $g(x) = 4x(1-x)$ with suitable domains. Find $(f \circ g)$ and $(g \circ f)$.

Published on 16 Apr 2020 - 8:52

score 127 · Answer 8 · 2026-03-31 03:33:33

127

Views

If a sentence $\varphi$ is true in all enumerable models, then is $\varphi$ true in all non-enumerable models too?

Published on 31 Mar 2026 - 3:33

score 72 · Answer 9 · 2020-04-16 11:44:39

72

Views

Prove that $(\alpha, \beta)^T$ is a point on a circle

Published on 16 Apr 2020 - 11:44

score 147 · Answer 10 · 2026-04-03 03:00:39

147

Views

If $A, B$ forms a separation of $X$, does $A \cap Y$ and $B \cap Y$ forms a separation of Y when they are non-empty?

Published on 03 Apr 2026 - 3:00

score 2k · Answer 11 · 2020-04-16 12:30:05

2k

Views

Prove that for all real numbers x and y we have $| |x| - |y| | \leq |x-y|$.

Published on 16 Apr 2020 - 12:30

score 224 · Answer 12 · 2020-04-16 12:40:33

224

Views

Is this a good enough proof by induction?

Published on 16 Apr 2020 - 12:40

score 1.3k · Answer 13 · 2020-04-16 16:34:20

1.3k

Views

Is it valid to use operations on both sides before inequality is proven?

Published on 16 Apr 2020 - 16:34

score 101 · Answer 14 · 2026-03-25 12:47:19

101

Views

Reflection through affine subspace

Published on 25 Mar 2026 - 12:47

score 50 · Answer 15 · 2026-04-03 03:00:15

50

Views

If $X$ has a open-closed base $\mathcal{B}$ and if $|X|>1$ then $X$ is not locally connected

Published on 03 Apr 2026 - 3:00

List Question

Prove the Positive Orthant is Open (Proof Verification)

Proof verification: Let $a_{n}$ be a sequence of real numbers bounded by $M\in\textbf{R}$, and which is also increasing. Then $a_{n}$ is convergent.

Is $\displaystyle \sum_{k = 1}^n\frac{1}{k^2} \leq 2 -\frac{1}{n}$ correctly proved by induction?

Suppose the sequences $a_{n}$ and $b_{n}$ converge to $a$ and $b$, respectively. Then the sequence $(a_{n}b_{n})_{n=m}^{\infty}$ converges to $ab$.

A problem on nowhere dense sets in metric spaces.

Show that there is a $c\in(0,1)$ such that $f(c)=\int_0^cf(x)dx$.

Let $f(x) = \frac{1-x}{1+x}$ and $g(x) = 4x(1-x)$ with suitable domains. Find $(f \circ g)$ and $(g \circ f)$.

If a sentence $\varphi$ is true in all enumerable models, then is $\varphi$ true in all non-enumerable models too?

Prove that $(\alpha, \beta)^T$ is a point on a circle

If $A, B$ forms a separation of $X$, does $A \cap Y$ and $B \cap Y$ forms a separation of Y when they are non-empty?

Prove that for all real numbers x and y we have $| |x| - |y| | \leq |x-y|$.

Is this a good enough proof by induction?

Is it valid to use operations on both sides before inequality is proven?

Reflection through affine subspace

If $X$ has a open-closed base $\mathcal{B}$ and if $|X|>1$ then $X$ is not locally connected

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