Question

A question on the completeness of $(C[a,b], \sup)$ where $[a,b] \subset \mathbb{R}$

score 116 · Answer 1 · 2026-04-14 00:14:15

116

Views

A question on the completeness of $(C[a,b], \sup)$ where $[a,b] \subset \mathbb{R}$

Published on 14 Apr 2026 - 0:14

score 86 · Answer 2 · 2026-04-14 11:27:56

86

Views

Prove $ | \sum_{k=1}^{n} \frac{z_k}{k} |^2 \le ( \sum_{k=1}^{n} \frac{1}{k^2} ) (\sum_{k=1}^{n}| z_k|^2 ) $

Published on 14 Apr 2026 - 11:27

score 98 · Answer 3 · 2026-04-12 23:58:15

98

Views

Give a proof or a counter-example. A function f is analytic in an open set implies f being bounded there.

Published on 12 Apr 2026 - 23:58

score 2k · Answer 4 · 2026-04-10 21:30:16

2k

Views

If two functions are increasing is their product increasing?

Published on 10 Apr 2026 - 21:30

score 130 · Answer 5 · 2026-04-14 23:29:42

130

Views

Prove that $\frac{1}{2}(x+\frac{a}{x}) \ge \sqrt{a}$

Published on 14 Apr 2026 - 23:29

score 202 · Answer 6 · 2026-04-15 06:32:06

202

Views

Suppose $x$ and $y$ are natural numbers. Show that $xy$ odd implies that $x$ and $y$ are both odd.

Published on 15 Apr 2026 - 6:32

score 35 · Answer 7 · 2026-04-13 17:25:14

35

Views

Is $\mathbb{R}\setminus\{0\}$ endowed with $d(x,y)=|\frac{1}{x}-\frac{1}{y}|$ complete?

Published on 13 Apr 2026 - 17:25

score 1.1k · Answer 8 · 2026-04-12 03:06:54

1.1k

Views

How to use the terms "fixed", "arbitrary", "fixed but arbitrary", "given", "for all" ... in proofs

Published on 12 Apr 2026 - 3:06

score 460 · Answer 9 · 2026-04-16 14:29:34

460

Views

In proof writing, is it mathematically sound to prove uniqueness before proving existence?

Published on 16 Apr 2026 - 14:29

score 78 · Answer 10 · 2026-04-12 03:23:27

78

Views

Is my approach correct to this equation?

Published on 12 Apr 2026 - 3:23

score 120 · Answer 11 · 2026-04-15 23:18:30

120

Views

If $f \circ f = 0 $, show that transformations $f + id_x$ and $f - id_x$ are isomorphisms of $X$

Published on 15 Apr 2026 - 23:18

score 134 · Answer 12 · 2026-04-15 20:09:21

134

Views

$\sqrt{98} + 4^{\frac{1}{3}}$ is irrational

Published on 15 Apr 2026 - 20:09

score 2.7k · Answer 13 · 2026-04-25 13:06:15

Is it legitimate to specify a statement as a Theorem if it is proved using numerical methods (since it can't be proved analytically)?

score 41 · Answer 14 · 2026-04-14 10:29:26

41

Views

Discuss the existence and uniqueness of the following operator equation

Published on 14 Apr 2026 - 10:29

score 223 · Answer 15 · 2026-04-12 00:23:57

223

Views

The product topological space of two finite closed topologies is not finite closed.

Published on 12 Apr 2026 - 0:23

List Question

A question on the completeness of $(C[a,b], \sup)$ where $[a,b] \subset \mathbb{R}$

Prove $ | \sum_{k=1}^{n} \frac{z_k}{k} |^2 \le ( \sum_{k=1}^{n} \frac{1}{k^2} ) (\sum_{k=1}^{n}| z_k|^2 ) $

Give a proof or a counter-example. A function f is analytic in an open set implies f being bounded there.

If two functions are increasing is their product increasing?

Prove that $\frac{1}{2}(x+\frac{a}{x}) \ge \sqrt{a}$

Suppose $x$ and $y$ are natural numbers. Show that $xy$ odd implies that $x$ and $y$ are both odd.

Is $\mathbb{R}\setminus\{0\}$ endowed with $d(x,y)=|\frac{1}{x}-\frac{1}{y}|$ complete?

How to use the terms "fixed", "arbitrary", "fixed but arbitrary", "given", "for all" ... in proofs

In proof writing, is it mathematically sound to prove uniqueness before proving existence?

Is my approach correct to this equation?

If $f \circ f = 0 $, show that transformations $f + id_x$ and $f - id_x$ are isomorphisms of $X$

$\sqrt{98} + 4^{\frac{1}{3}}$ is irrational

Is it legitimate to specify a statement as a Theorem if it is proved using numerical methods (since it can't be proved analytically)?

Discuss the existence and uniqueness of the following operator equation

The product topological space of two finite closed topologies is not finite closed.

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