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Confusion about "$:=$" notation in pointwise convergence definition

score 87 · Answer 1 · 2026-04-09 01:59:21

87

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Confusion about "$:=$" notation in pointwise convergence definition

Published on 09 Apr 2026 - 1:59

score 76 · Answer 2 · 2026-02-24 21:02:33

76

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Does the sum of a sequence of functions $\{f_n(x)\}$ converge if the upper bound $h_n(x)$ with $f_n(x)\le h_n(x)$ converges pointwise to $0$?

Published on 24 Feb 2026 - 21:02

score 118 · Answer 3 · 2026-02-24 20:58:18

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Questions and observations regarding Putnam 2020 - A.6.

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score 85 · Answer 4 · 2026-04-12 21:29:54

85

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Proving that the infinite sum converges to $1$ as $k$ tends to infinity

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score 161 · Answer 5 · 2026-02-24 20:57:54

161

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Proving that convergence in RKHS implies pointwise convergence without using reproducing property

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score 66 · Answer 6 · 2026-02-24 21:02:33

66

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Convergence of $f_n(x) = \frac{\sqrt x (1-x)}{1+nx}$ and $g_n(x) = \sqrt n f_n(x)$

Published on 24 Feb 2026 - 21:02

score 23 · Answer 7 · 2026-02-24 21:00:27

23

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Pointwise ad unifrom convergence of $g_n : \mathbb R \times \mathbb R^+ \to \mathbb R$.

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score 48 · Answer 8 · 2026-02-24 20:56:19

48

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Some Locally Uniform Convergence

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score 29 · Answer 9 · 2026-02-24 20:54:35

29

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Proving numerical method 1st-order convergence

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score 97 · Answer 10 · 2026-04-10 07:08:52

97

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Whats the point of Pointwise Convergence

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score 44 · Answer 11 · 2026-02-24 21:00:13

44

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Show the sequence of functions (which can graphically be described as shrinking width triangles of height 1) converges pointwise to the zero function.

Published on 24 Feb 2026 - 21:00

score 87 · Answer 12 · 2026-02-24 21:02:23

87

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Does fourier series for $f(x)=\begin{cases}-1\ \text{for}\ x \in (-\pi, 0) \\0 \ \text{for}\ x=0 \\ 1 \ \text{for} \ x\in (0,\pi)\end{cases}$ converge

Published on 24 Feb 2026 - 21:02

score 80 · Answer 13 · 2026-02-24 21:03:46

80

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How to show that the series of functions $\sum_{k = 0}^\infty(-1)^k \frac{x^{2k + 1}}{2k + 1}$ is pointwise convergent to a function?

Published on 24 Feb 2026 - 21:03

score 53 · Answer 14 · 2026-02-24 21:02:22

53

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Convergence of a series of the product of two functions when one of them is shifted by one

Published on 24 Feb 2026 - 21:02

score 42 · Answer 15 · 2026-04-11 17:46:03

42

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Question on pointwise convergence and norms

Published on 11 Apr 2026 - 17:46

List Question

Confusion about "$:=$" notation in pointwise convergence definition

Does the sum of a sequence of functions $\{f_n(x)\}$ converge if the upper bound $h_n(x)$ with $f_n(x)\le h_n(x)$ converges pointwise to $0$?

Questions and observations regarding Putnam 2020 - A.6.

Proving that the infinite sum converges to $1$ as $k$ tends to infinity

Proving that convergence in RKHS implies pointwise convergence without using reproducing property

Convergence of $f_n(x) = \frac{\sqrt x (1-x)}{1+nx}$ and $g_n(x) = \sqrt n f_n(x)$

Pointwise ad unifrom convergence of $g_n : \mathbb R \times \mathbb R^+ \to \mathbb R$.

Some Locally Uniform Convergence

Proving numerical method 1st-order convergence

Whats the point of Pointwise Convergence

Show the sequence of functions (which can graphically be described as shrinking width triangles of height 1) converges pointwise to the zero function.

Does fourier series for $f(x)=\begin{cases}-1\ \text{for}\ x \in (-\pi, 0) \\0 \ \text{for}\ x=0 \\ 1 \ \text{for} \ x\in (0,\pi)\end{cases}$ converge

How to show that the series of functions $\sum_{k = 0}^\infty(-1)^k \frac{x^{2k + 1}}{2k + 1}$ is pointwise convergent to a function?

Convergence of a series of the product of two functions when one of them is shifted by one

Question on pointwise convergence and norms

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