Question

Prove the sequence $f_{n} = \frac{1}{n^2+1}$ is a Cauchy sequence.

score 354 · Answer 1 · 2026-04-16 20:53:09

354

Views

Prove the sequence $f_{n} = \frac{1}{n^2+1}$ is a Cauchy sequence.

Published on 16 Apr 2026 - 20:53

score 48 · Answer 2 · 2026-04-10 23:01:18

48

Views

Attempt at showing the structure of a proof of : " A well ordered set is totally ordered"

Published on 10 Apr 2026 - 23:01

score 38 · Answer 3 · 2026-04-17 06:10:29

38

Views

Compute $\int_{t-2T}^T t-\tau\cdot 1 \;d\tau = [t\tau - \frac{\tau^2}{2}]_{t-2T}^{T}$

Published on 17 Apr 2026 - 6:10

score 95 · Answer 4 · 2026-04-16 20:03:57

95

Views

$f: [0,1] \to \mathbb{R}$ such that $f(x)=1$ if $x=\frac{1}{2},\frac{1}{4},...$ and $f(x)=0$ else is integrable

Published on 16 Apr 2026 - 20:03

score 151 · Answer 5 · 2026-04-17 05:34:25

151

Views

Find for given supremum, epsilon.

Published on 17 Apr 2026 - 5:34

score 323 · Answer 6 · 2026-05-11 07:47:23

323

Views

Let $A$ be a $101$-element subset of the set $S=\{1,2,\ldots,1000000\}$

Published on 11 May 2026 - 7:47

score 45 · Answer 7 · 2026-04-14 02:32:28

45

Views

Prove $x<y \Rightarrow x+z < y+z$ with $x,y,z \in \mathbb{K}$ when $\mathbb{K}$ is an ordered field.

Published on 14 Apr 2026 - 2:32

score 107 · Answer 8 · 2026-04-15 02:29:39

107

Views

Solving a set of multivariate polynomials; four equations, four unknowns, maximum degree 2

Published on 15 Apr 2026 - 2:29

score 54 · Answer 9 · 2026-05-10 15:46:47

54

Views

Prove $x=y ⇔ x≤y ∧ x≥y$ with $x,y \in \mathbb{K}$ if $ \mathbb{K}$ is an ordered field.

Published on 10 May 2026 - 15:46

score 2.9k · Answer 10 · 2026-04-12 18:40:37

2.9k

Views

If every nonidentity element in a group is of order $2$, the group is abelian

Published on 12 Apr 2026 - 18:40

score 906 · Answer 11 · 2026-04-13 09:30:20

906

Views

Testing divisibility by 7 of number in base 8

Published on 13 Apr 2026 - 9:30

score 64 · Answer 12 · 2026-05-11 03:28:29

64

Views

Prove $F(x)=\cos(x^{-1})\cdot\mathbf1_{x>0}$ is not of Bounded Variation on $[0,1]$

Published on 11 May 2026 - 3:28

score 67 · Answer 13 · 2026-05-10 18:41:41

67

Views

sufficient condition for discrete valuation ring

Published on 10 May 2026 - 18:41

score 130 · Answer 14 · 2026-05-11 05:08:58

130

Views

need help solving geometric series questions

Published on 11 May 2026 - 5:08

score 82 · Answer 15 · 2026-04-16 14:42:10

82

Views

What am I doing wrong in evaluating $\int {\frac {dx}{1+x-x^2}}$?

Published on 16 Apr 2026 - 14:42

List Question

Prove the sequence $f_{n} = \frac{1}{n^2+1}$ is a Cauchy sequence.

Attempt at showing the structure of a proof of : " A well ordered set is totally ordered"

Compute $\int_{t-2T}^T t-\tau\cdot 1 \;d\tau = [t\tau - \frac{\tau^2}{2}]_{t-2T}^{T}$

$f: [0,1] \to \mathbb{R}$ such that $f(x)=1$ if $x=\frac{1}{2},\frac{1}{4},...$ and $f(x)=0$ else is integrable

Find for given supremum, epsilon.

Let $A$ be a $101$-element subset of the set $S=\{1,2,\ldots,1000000\}$

Prove $x<y \Rightarrow x+z < y+z$ with $x,y,z \in \mathbb{K}$ when $\mathbb{K}$ is an ordered field.

Solving a set of multivariate polynomials; four equations, four unknowns, maximum degree 2

Prove $x=y ⇔ x≤y ∧ x≥y$ with $x,y \in \mathbb{K}$ if $ \mathbb{K}$ is an ordered field.

If every nonidentity element in a group is of order $2$, the group is abelian

Testing divisibility by 7 of number in base 8

Prove $F(x)=\cos(x^{-1})\cdot\mathbf1_{x>0}$ is not of Bounded Variation on $[0,1]$

sufficient condition for discrete valuation ring

need help solving geometric series questions

What am I doing wrong in evaluating $\int {\frac {dx}{1+x-x^2}}$?

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