User Michael

11 votes

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Why is the range a larger set than the domain?

answered Mar 26, 2022 at 1:08

10 votes

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Does real analysis have new theorems, or is it just a collection of proofs of old calculus theorems?

answered May 17, 2023 at 21:38

6 votes

Let $Y$ be an ordered set in the order topology with $f,g:X\rightarrow Y$ continuous, show that $\{x:f(x)\leq g(x)\}$ is closed in $X$

answered Jun 8, 2019 at 1:09

4 votes

Sequence $\lim_{n\to\infty}(-1)^{n} \frac{\sin (n)}{n^2}$

answered Apr 1, 2019 at 18:43

4 votes

Group action definition

answered Feb 4, 2021 at 3:35

4 votes

Well-defined set in naive set theory

answered Jun 16, 2023 at 19:36

4 votes

Why do we teach linear algebra in precalculus classes?

answered May 11, 2023 at 1:24

4 votes

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Understanding notation of norm with three vertical lines

answered Dec 17, 2022 at 15:11

3 votes

Why is the graph of $sec^2(x)/tan^2(x)$ continuous at $x=\pi /2$?

answered Jun 1, 2021 at 2:55

3 votes

Integration simple question

answered Sep 9, 2019 at 2:51

3 votes

How to find the order of a symmetric group S4?

answered Feb 27, 2019 at 1:19

2 votes

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Finding the Shape of a Graph Using the Min and Max

answered Nov 14, 2018 at 0:49

2 votes

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Determine which of the following are open sets in $\mathbb{R}l$. In each case, prove your assertion

answered Jun 13, 2019 at 20:59

2 votes

Theorem 9.17 from Baby Rudin

answered Apr 20, 2023 at 23:40

2 votes

Showing the sequence $\sqrt{2}, \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}, \dots$ tends to $2$ using the Epsilon-Neighbourhood definition

answered Feb 9, 2021 at 7:48

2 votes

Let $G$ be a group and if $a,b \in G$ such that $a^4 =e$ and $a^2 b=ba$ then prove that $a=e$

answered Jun 1, 2021 at 3:22

2 votes

Doubt about Artin’s Algebra Theorem 2.3.3 Proof

answered Jan 7, 2022 at 9:19

2 votes

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What does it mean that two differentiable structures are distinct?

answered Aug 19, 2023 at 23:59

2 votes

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Showing that $u_n=\sum_{k=0}^{n}\frac{1}{k!}$ is Cauchy

answered Dec 24, 2022 at 17:45

2 votes

How do I show $\lim\limits_{x\to\infty}{\frac{x^{3}+x}{2+4x^3}} = \frac{1}{4}$ with the definition of $\lim\limits_{x \to \infty}f(x)$?

answered Nov 22, 2022 at 10:09

2 votes

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In a sequence if a successor $s_{n+1} \lt \frac{1}{2}\cdot s_n$ holds for each n, then $s_{n+1} \lt \frac{1}{2^{n}}\cdot s_1$ why is this true?

answered Jul 2 at 23:24

2 votes

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Find the smallest positive integer $N$ such that $z^N$ is a real number

answered Jun 21, 2023 at 15:16

2 votes

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Why does "Any bounded sequence $(x_n)⊂H$ contains a sub-sequence $(x_{n_k} )$ such that $(Cx_{n_k} )$ converges."?

answered Dec 16, 2022 at 4:37

2 votes

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Is this result correct?

answered Dec 27, 2022 at 2:50

1 vote

Prove that the sequence ($s_n$) is convergent if |$s_{n+1}$-$s_n$|<${1}/{2^n}$: Is my proof correct?

answered Jun 17, 2023 at 17:21

1 vote

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Is a bounded sequence to some power also a bounded sequence

answered Sep 4, 2023 at 18:27

1 vote

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Help in proving that the closure of intersection is contained in the intersection of the closures

answered Dec 15, 2022 at 5:18

1 vote

Proving an inequality with logs and L'Hopital Rule

answered Mar 11, 2019 at 2:04

1 vote

Open/compact sets in metric $d_1$ and $d_2$

answered May 27, 2021 at 13:41

1 vote

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Why aren't equations with rational expressions equivalent to different forms?

answered Dec 24, 2022 at 22:07

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63 Answers

Why is the range a larger set than the domain?

Does real analysis have new theorems, or is it just a collection of proofs of old calculus theorems?

Let $Y$ be an ordered set in the order topology with $f,g:X\rightarrow Y$ continuous, show that $\{x:f(x)\leq g(x)\}$ is closed in $X$

Sequence $\lim_{n\to\infty}(-1)^{n} \frac{\sin (n)}{n^2}$

Group action definition

Well-defined set in naive set theory

Why do we teach linear algebra in precalculus classes?

Understanding notation of norm with three vertical lines

Why is the graph of $sec^2(x)/tan^2(x)$ continuous at $x=\pi /2$?

Integration simple question

How to find the order of a symmetric group S4?

Finding the Shape of a Graph Using the Min and Max

Determine which of the following are open sets in $\mathbb{R}l$. In each case, prove your assertion

Theorem 9.17 from Baby Rudin

Showing the sequence $\sqrt{2}, \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}, \dots$ tends to $2$ using the Epsilon-Neighbourhood definition

Let $G$ be a group and if $a,b \in G$ such that $a^4 =e$ and $a^2 b=ba$ then prove that $a=e$

Doubt about Artin’s Algebra Theorem 2.3.3 Proof

What does it mean that two differentiable structures are distinct?

Showing that $u_n=\sum_{k=0}^{n}\frac{1}{k!}$ is Cauchy

How do I show $\lim\limits_{x\to\infty}{\frac{x^{3}+x}{2+4x^3}} = \frac{1}{4}$ with the definition of $\lim\limits_{x \to \infty}f(x)$?

In a sequence if a successor $s_{n+1} \lt \frac{1}{2}\cdot s_n$ holds for each n, then $s_{n+1} \lt \frac{1}{2^{n}}\cdot s_1$ why is this true?

Find the smallest positive integer $N$ such that $z^N$ is a real number

Why does "Any bounded sequence $(x_n)⊂H$ contains a sub-sequence $(x_{n_k} )$ such that $(Cx_{n_k} )$ converges."?

Is this result correct?

Prove that the sequence ($s_n$) is convergent if |$s_{n+1}$-$s_n$|<${1}/{2^n}$: Is my proof correct?

Is a bounded sequence to some power also a bounded sequence

Help in proving that the closure of intersection is contained in the intersection of the closures

Proving an inequality with logs and L'Hopital Rule

Open/compact sets in metric $d_1$ and $d_2$

Why aren't equations with rational expressions equivalent to different forms?