Question

Proving that family of fractions is dense in $\mathbb{R}$

score 120 · Answer 1 · 2018-03-18 22:15:58

120

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Proving that family of fractions is dense in $\mathbb{R}$

Published on 18 Mar 2018 - 22:15

score 32 · Answer 2 · 2026-03-27 01:47:37

32

Views

Confirmation of Proof: $\forall a,b \in\mathbb{R}, \ \sum_{n=0}^\infty \frac{a}{b^n} = \frac{ab}{b-1}\Leftrightarrow \frac b2\in(1, a].$

Published on 27 Mar 2026 - 1:47

score 30 · Answer 3 · 2026-03-26 10:46:15

30

Views

Proving transitivity on a relation defined as there exist $u,v \in \mathbb{N} : x^u = y^v$

Published on 26 Mar 2026 - 10:46

score 103 · Answer 4 · 2018-03-19 18:18:04

103

Views

Use fundamental theorem of calculus to prove ${f'(x)}=\lim_{n\to \infty}{f'_n(x)}$ for all $x\in{[a,b]}$

Published on 19 Mar 2018 - 18:18

score 43 · Answer 5 · 2026-03-27 00:05:05

43

Views

Proof for inequality involving mean of $k$ closest values

Published on 27 Mar 2026 - 0:05

score 70 · Answer 6 · 2018-03-19 19:43:23

70

Views

Is the procedure for proving $A = B$ the same as for proving $A \iff B$?

Published on 19 Mar 2018 - 19:43

score 228 · Answer 7 · 2026-04-10 20:56:14

228

Views

What does it mean to "fix" an orthonormal basis?

Published on 10 Apr 2026 - 20:56

score 2.1k · Answer 8 · 2026-04-06 16:48:57

2.1k

Views

Nested induction

Published on 06 Apr 2026 - 16:48

score 8.2k · Answer 9 · 2026-04-12 02:46:10

8.2k

Views

Prove $\cos(x)$ is continuous

Published on 12 Apr 2026 - 2:46

score 79 · Answer 10 · 2026-04-10 23:47:33

79

Views

What does the term "bijective proof" mean in mathematics and how I can construct one?

Published on 10 Apr 2026 - 23:47

score 60 · Answer 11 · 2018-03-20 15:50:10

60

Views

Let ≤ be an ordering on a set A. Prove that if ≤ is a well-ordering then it is a linear-ordering.

Published on 20 Mar 2018 - 15:50

score 54 · Answer 12 · 2018-03-20 16:27:53

54

Views

Show $\lim_{x \to 4} \frac{x^2 - 16}{x-4} = 8$

Published on 20 Mar 2018 - 16:27

score 2.8k · Answer 13 · 2026-03-29 12:40:34

2.8k

Views

A closed ball in a metric space is closed

Published on 29 Mar 2026 - 12:40

score 2.2k · Answer 14 · 2026-04-10 22:28:04

2.2k

Views

Perfect square as sum of two perfect squares

Published on 10 Apr 2026 - 22:28

score 5k · Answer 15 · 2026-04-11 16:43:51

5k

Views

How many words (i.e. not "math" symbols") should I use in my proofs? ${}{}$

Published on 11 Apr 2026 - 16:43

List Question

Proving that family of fractions is dense in $\mathbb{R}$

Confirmation of Proof: $\forall a,b \in\mathbb{R}, \ \sum_{n=0}^\infty \frac{a}{b^n} = \frac{ab}{b-1}\Leftrightarrow \frac b2\in(1, a].$

Proving transitivity on a relation defined as there exist $u,v \in \mathbb{N} : x^u = y^v$

Use fundamental theorem of calculus to prove ${f'(x)}=\lim_{n\to \infty}{f'_n(x)}$ for all $x\in{[a,b]}$

Proof for inequality involving mean of $k$ closest values

Is the procedure for proving $A = B$ the same as for proving $A \iff B$?

What does it mean to "fix" an orthonormal basis?

Nested induction

Prove $\cos(x)$ is continuous

What does the term "bijective proof" mean in mathematics and how I can construct one?

Let ≤ be an ordering on a set A. Prove that if ≤ is a well-ordering then it is a linear-ordering.

Show $\lim_{x \to 4} \frac{x^2 - 16}{x-4} = 8$

A closed ball in a metric space is closed

Perfect square as sum of two perfect squares

How many words (i.e. not "math" symbols") should I use in my proofs? ${}{}$

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