List questions from alternative-proof

Published on 11 Apr 2026 - 8:57

172

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Ways to show $\int_0^{\infty}\frac{\sin^2(\pi x)}{x^2}\Big\lvert x-\Big\lfloor x +\frac12 \Big\rfloor \Big\rvert \, \mathrm{d}x = \frac{\pi^2}{8}$?

Published on 17 Apr 2026 - 9:13

124

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Alternative Solution to Theorem 5 Corollary 2, Section 2.3 of Hoffman’s Linear Algebra

Published on 12 Apr 2026 - 20:55

119

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(Generalized) Cantor set is uncountable

Published on 14 Apr 2026 - 15:39

174

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Theorem 6, Section 2.3 of Hoffman and Kunze’s Linear Algebra

Published on 09 Apr 2026 - 16:52

28

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Deriving the formula for the number of distinct de Bruijn sequences

Published on 14 Apr 2026 - 5:54

128

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There are only finitely many integer lattices with bounded covolume

Published on 15 Apr 2026 - 4:47

92

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Different Characterization of Basis of a Vector Space

Published on 14 Apr 2026 - 3:27

97

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Showing $ \left \lceil \frac{a}{b} \right \rceil \leq \frac{a+b-1}{b}$

Published on 14 Apr 2026 - 17:02

176

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A more elegant way to prove an Euclidean geometry theorem

Published on 14 Apr 2026 - 10:36

97

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Derivation of the Euler-Lagrange equation using an infinite sum

Published on 12 Apr 2026 - 11:27

107

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(GD)Let $\alpha: I \to \mathbb R^n (n = 2, 3)$ be a regular curve of any parameter $r \in I$...

Published on 15 Apr 2026 - 5:31

55

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Proof involving composing sums with itself.

Published on 10 Apr 2026 - 23:53

326

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Is there anything wrong with this proof that $\lim_{x\to0} \frac{\sin(x)}{x} = 1$?

Published on 16 Apr 2026 - 14:42

118

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Calculate $\lim_{n\to\infty}\int_0^1 f(\{nx^k\})g(x^n)\,dx$.

Published on 17 Apr 2026 - 8:52

List Question

Closed form for $\sum_{k=1}^\infty\frac{H_k^{(m)}}{k^n}$

Ways to show $\int_0^{\infty}\frac{\sin^2(\pi x)}{x^2}\Big\lvert x-\Big\lfloor x +\frac12 \Big\rfloor \Big\rvert \, \mathrm{d}x = \frac{\pi^2}{8}$?

Alternative Solution to Theorem 5 Corollary 2, Section 2.3 of Hoffman’s Linear Algebra

(Generalized) Cantor set is uncountable

Theorem 6, Section 2.3 of Hoffman and Kunze’s Linear Algebra

Deriving the formula for the number of distinct de Bruijn sequences

There are only finitely many integer lattices with bounded covolume

Different Characterization of Basis of a Vector Space

Showing $ \left \lceil \frac{a}{b} \right \rceil \leq \frac{a+b-1}{b}$

A more elegant way to prove an Euclidean geometry theorem

Derivation of the Euler-Lagrange equation using an infinite sum

(GD)Let $\alpha: I \to \mathbb R^n (n = 2, 3)$ be a regular curve of any parameter $r \in I$...

Proof involving composing sums with itself.

Is there anything wrong with this proof that $\lim_{x\to0} \frac{\sin(x)}{x} = 1$?

Calculate $\lim_{n\to\infty}\int_0^1 f(\{nx^k\})g(x^n)\,dx$.

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