Question

Change of quantifiers in the definition of continuity.

score 188 · Answer 1 · 2026-04-10 23:28:38

188

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Change of quantifiers in the definition of continuity.

Published on 10 Apr 2026 - 23:28

score 142 · Answer 2 · 2026-04-12 13:04:14

142

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How can I prove that $\mathbb{S}_{+}^n$ is a closed and convex set?

Published on 12 Apr 2026 - 13:04

score 206 · Answer 3 · 2026-04-16 14:01:15

206

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Stolz-Cesàro $0/0$ case: is $\limsup \frac{a_n}{b_n}\le \limsup\frac{a_{n+1}-a_n}{b_{n+1}-b_n}$?

Published on 16 Apr 2026 - 14:01

score 79 · Answer 4 · 2026-04-17 00:33:08

79

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Evaluate $\lim\limits_{x \to 1}\dfrac{x-x^x}{1-x+\ln x}$.

Published on 17 Apr 2026 - 0:33

score 40 · Answer 5 · 2026-04-10 05:49:11

40

Views

Induction Proof Verification

Published on 10 Apr 2026 - 5:49

score 454 · Answer 6 · 2026-04-14 23:11:52

454

Views

Showing that $f(x)=x$ for at least one point in $[0,1]$

Published on 14 Apr 2026 - 23:11

score 118 · Answer 7 · 2026-04-16 07:46:30

118

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Is there a set of three linearly independent vectors in $\mathbb{C}^2$?

Published on 16 Apr 2026 - 7:46

score 104 · Answer 8 · 2026-04-14 20:46:37

104

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A complete ordered field has a unique ordering

Published on 14 Apr 2026 - 20:46

score 115 · Answer 9 · 2026-04-29 01:42:19

115

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How to show $x_1y_1 + x_2y_2 - (x_3y_3 + x_4y_4) > 0$

Published on 29 Apr 2026 - 1:42

score 576 · Answer 10 · 2026-04-16 06:06:40

576

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If $x$ and $y$ are arbitrary real numbers with $x < y$, prove that there exists at least one real satisfying $x < z < y$

Published on 16 Apr 2026 - 6:06

score 68 · Answer 11 · 2026-04-16 14:03:53

68

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Proof that $\int_{0}^{1}\frac{1}{x-\ln(x)}\mathbb{d}x$ is convergent.

Published on 16 Apr 2026 - 14:03

score 118 · Answer 12 · 2026-04-17 12:16:21

118

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Prove $\lim_{n\to\infty}(|x_n + y_n| - |x_n - y_n|) = +\infty \iff \lim_{n\to\infty}|x_n| =\lim_{n\to\infty}|y_n| =\lim_{n\to\infty}x_ny_n =+\infty$

Published on 17 Apr 2026 - 12:16

score 28 · Answer 13 · 2026-04-11 23:57:00

28

Views

Verification of metric axiom 3

Published on 11 Apr 2026 - 23:57

score 53 · Answer 14 · 2026-04-17 13:36:12

53

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On cardinality: $|[0,1]|\ge|\{0,1\}^{\mathbb{N}}|$ and $|\{0,1\}^{\mathbb{N}}|\ge |(0,1)|$

Published on 17 Apr 2026 - 13:36

score 69 · Answer 15 · 2026-04-13 17:53:04

69

Views

How many functions can be made with the following sets?

Published on 13 Apr 2026 - 17:53

List Question

Change of quantifiers in the definition of continuity.

How can I prove that $\mathbb{S}_{+}^n$ is a closed and convex set?

Stolz-Cesàro $0/0$ case: is $\limsup \frac{a_n}{b_n}\le \limsup\frac{a_{n+1}-a_n}{b_{n+1}-b_n}$?

Evaluate $\lim\limits_{x \to 1}\dfrac{x-x^x}{1-x+\ln x}$.

Induction Proof Verification

Showing that $f(x)=x$ for at least one point in $[0,1]$

Is there a set of three linearly independent vectors in $\mathbb{C}^2$?

A complete ordered field has a unique ordering

How to show $x_1y_1 + x_2y_2 - (x_3y_3 + x_4y_4) > 0$

If $x$ and $y$ are arbitrary real numbers with $x < y$, prove that there exists at least one real satisfying $x < z < y$

Proof that $\int_{0}^{1}\frac{1}{x-\ln(x)}\mathbb{d}x$ is convergent.

Prove $\lim_{n\to\infty}(|x_n + y_n| - |x_n - y_n|) = +\infty \iff \lim_{n\to\infty}|x_n| =\lim_{n\to\infty}|y_n| =\lim_{n\to\infty}x_ny_n =+\infty$

Verification of metric axiom 3

On cardinality: $|[0,1]|\ge|\{0,1\}^{\mathbb{N}}|$ and $|\{0,1\}^{\mathbb{N}}|\ge |(0,1)|$

How many functions can be made with the following sets?

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