User niobium - Mathematics Stack Exchange

6 votes

2 answers

92 views

Difference betwwen $(\sqrt{2}, \pi)\cap \mathbb Q$ and $[\sqrt{2}, \pi]\cap \mathbb Q$ in $\mathbb Q$

asked Apr 4, 2023 at 8:33

5 votes

3 answers

703 views

Why probability distribution is defined on event space and not on sample space?

asked Nov 29, 2022 at 14:59

4 votes

3 answers

197 views

Rudin 3.29 the series $\sum_{n=3}^{\infty} \frac{1}{n \ln n(\ln(\ln n))^2}$ converges

asked Mar 9, 2023 at 15:07

4 votes

3 answers

172 views

Two double sums must be equal, struggle with indices

asked Mar 13, 2023 at 19:34

4 votes

3 answers

163 views

Rudin PMA 4.20 - how can this function be unbounded ? Considering Rudin hasn't introduced "divergence" of functions yet in the chapter.

asked Mar 31, 2023 at 17:11

4 votes

0 answers

154 views

Chinese remainder theorem, how does one justify the existence of the solution, without intuiting it?

asked Oct 28, 2023 at 15:40

3 votes

2 answers

81 views

Rudin $7.14$ linked to $7.9$ why does Rudin make boundedness compulsory in uniform convergence?

asked Jul 28, 2023 at 9:47

3 votes

1 answer

67 views

Assigning to every odd number a triangular number. Does the converse hold?

asked Sep 3, 2023 at 19:49

3 votes

2 answers

92 views

Is ∞ a limit point of $\mathbb R$ ? If not, how to understand Rudin's definition at the beginning of chapter $4$ (PMA)?

asked Mar 26, 2023 at 12:29

3 votes

1 answer

282 views

Cantor set - is it made of $[a,b]$ intervals or exclusively of singletons?

asked Feb 10, 2023 at 14:37

3 votes

3 answers

119 views

Can you prove this equality? Binomial coefficients and probability frequency

asked Feb 4, 2022 at 10:05

3 votes

1 answer

86 views

Is this definition of local continuity (with open sets) accurate?

asked Dec 23, 2022 at 8:19

2 votes

3 answers

151 views

Quantifiers in contrapositive of transitivity of "divide" relation

asked Oct 14, 2022 at 10:51

2 votes

2 answers

58 views

Congruence. How would you prove this set equality? (congruence division) [duplicate]

asked Oct 23, 2022 at 12:22

2 votes

1 answer

686 views

Trying to prove delta function is 0 outside of 0

asked Sep 3, 2022 at 16:15

2 votes

1 answer

101 views

Change of variable $2\pi$ in the Fourier Transform

asked Sep 10, 2022 at 15:54

2 votes

1 answer

40 views

Looking for a proof that a set limit point of the range of a sequence, is a sequence limit point for this sequence

asked Feb 18, 2023 at 15:39

2 votes

1 answer

119 views

Proof of Riemann's theorem of Rudin how to show that $\alpha$ and $\beta$ are the $\lim \sup$ and $\lim \inf$ - need help to end my proof

asked Mar 22, 2023 at 12:19

2 votes

0 answers

65 views

Alternative book for "infinite limits and limits at infinity" for a real function ? (Rudin PMA 4.33)

asked Apr 13, 2023 at 17:41

2 votes

2 answers

41 views

In L'Hospital rule should we specify $g(x) \ne 0$ on $(a,b)$ in the theorem to avoid division by $0$? Does $g'(x)\ne 0$ imply $g(x)\ne 0$ on $(a,b)$?

asked May 16, 2023 at 9:46

2 votes

1 answer

57 views

Equivalence of two different formulations of neighborhood systems in a set

asked Jun 15, 2023 at 10:44

2 votes

1 answer

49 views

Why $\nabla f$ do not exactly coincide with $D f$ (it's its transpose)

asked May 16 at 9:12

1 vote

0 answers

31 views

How to prove $p$ is in the confidence interval $[f-1/ \sqrt{n},f+1/ \sqrt{n}]$ where $f$ is one possible value of $\sum X_i /n$?

asked Apr 19 at 6:45

1 vote

2 answers

69 views

$\{r\in \mathbb Q \mid r^2 <2 \}$ has $\{r\in \mathbb Q \mid r^2 >2 \}$ as its set of upper bounds

asked Jan 13 at 10:05

1 vote

1 answer

23 views

Finding $\lim_{x\to 0} x \ln(x)$ via $\lim_{x\to -\infty} x \exp(x)$ - is the composition to the right licit?

asked Mar 9 at 14:03

1 vote

1 answer

31 views

Finding the limit of $\arctan(x)^{\frac{1}{x^2}}$ as $x$ tends to $0$ using Taylor expansions

asked Jun 25, 2023 at 17:09

1 vote

0 answers

21 views

Rudin $9.3(a)$'s led me to a question about the existence logic quantifier and it's variables

asked Jun 29, 2023 at 8:55

1 vote

2 answers

91 views

Operator norm $4$ different definitions how to prove that $\sup$ is $\max$ and $\inf$ is $\min$ for the last two?

asked Jul 2, 2023 at 16:42

1 vote

1 answer

99 views

Rudin $9.21$ why do we treat only the $m=1$ case in the converse?

asked Jul 11, 2023 at 10:28

1 vote

1 answer

86 views

Strong induction to prove a finite poset has at least one maximal element - two questions

asked May 29, 2023 at 10:33

Stack Exchange Network

125 Questions

Difference betwwen $(\sqrt{2}, \pi)\cap \mathbb Q$ and $[\sqrt{2}, \pi]\cap \mathbb Q$ in $\mathbb Q$

Why probability distribution is defined on event space and not on sample space?

Rudin 3.29 the series $\sum_{n=3}^{\infty} \frac{1}{n \ln n(\ln(\ln n))^2}$ converges

Two double sums must be equal, struggle with indices

Rudin PMA 4.20 - how can this function be unbounded ? Considering Rudin hasn't introduced "divergence" of functions yet in the chapter.

Chinese remainder theorem, how does one justify the existence of the solution, without intuiting it?

Rudin $7.14$ linked to $7.9$ why does Rudin make boundedness compulsory in uniform convergence?

Assigning to every odd number a triangular number. Does the converse hold?

Is ∞ a limit point of $\mathbb R$ ? If not, how to understand Rudin's definition at the beginning of chapter $4$ (PMA)?

Cantor set - is it made of $[a,b]$ intervals or exclusively of singletons?

Can you prove this equality? Binomial coefficients and probability frequency

Is this definition of local continuity (with open sets) accurate?

Quantifiers in contrapositive of transitivity of "divide" relation

Congruence. How would you prove this set equality? (congruence division) [duplicate]

Trying to prove delta function is 0 outside of 0

Change of variable $2\pi$ in the Fourier Transform

Looking for a proof that a set limit point of the range of a sequence, is a sequence limit point for this sequence

Proof of Riemann's theorem of Rudin how to show that $\alpha$ and $\beta$ are the $\lim \sup$ and $\lim \inf$ - need help to end my proof

Alternative book for "infinite limits and limits at infinity" for a real function ? (Rudin PMA 4.33)

In L'Hospital rule should we specify $g(x) \ne 0$ on $(a,b)$ in the theorem to avoid division by $0$? Does $g'(x)\ne 0$ imply $g(x)\ne 0$ on $(a,b)$?

Equivalence of two different formulations of neighborhood systems in a set

Why $\nabla f$ do not exactly coincide with $D f$ (it's its transpose)

How to prove $p$ is in the confidence interval $[f-1/ \sqrt{n},f+1/ \sqrt{n}]$ where $f$ is one possible value of $\sum X_i /n$?

$\{r\in \mathbb Q \mid r^2 <2 \}$ has $\{r\in \mathbb Q \mid r^2 >2 \}$ as its set of upper bounds

Finding $\lim_{x\to 0} x \ln(x)$ via $\lim_{x\to -\infty} x \exp(x)$ - is the composition to the right licit?

Finding the limit of $\arctan(x)^{\frac{1}{x^2}}$ as $x$ tends to $0$ using Taylor expansions

Rudin $9.3(a)$'s led me to a question about the existence logic quantifier and it's variables

Operator norm $4$ different definitions how to prove that $\sup$ is $\max$ and $\inf$ is $\min$ for the last two?

Rudin $9.21$ why do we treat only the $m=1$ case in the converse?

Strong induction to prove a finite poset has at least one maximal element - two questions