List questions from alternative-proof

Published on 12 Apr 2026 - 19:01

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Finding an alternative nicer method to evaluate the summation

Published on 12 Apr 2026 - 11:56

165

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Induction proof that the $n$-sphere $S^{n}$ is connected

Published on 15 Apr 2026 - 13:35

60

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Suppose $\ a,b\in\mathbb{Q}^+.\ $ Then $\ \exists\ c,d,k\in\mathbb{Z}^+,\ $ such that $\ a = \frac{c}{k},\ b = \frac{d}{k}\ $ and $\ \gcd(c,d,k)=1.$

Published on 16 Apr 2026 - 7:02

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Need verification (and an alternative, if that's possible) for proof on generalization of direct sum

Published on 15 Apr 2026 - 15:37

90

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Any hints to shortly prove that $f(x) = (x^2-1)^2 \cosh2 x-(x^2+1)^2$ crosses the $x$ axis only once?

Published on 15 Apr 2026 - 20:15

557

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Can this intuitive explanation of the Change of Variable Theorem be turned into a proof?

Published on 12 Apr 2026 - 4:54

230

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Equation of a plane in normal form

Published on 25 Apr 2026 - 2:31

53

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A Countable Union of Closed Set that is Actually Closed

Published on 11 Apr 2026 - 18:47

155

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Prove that 1 divides every integer, and that every integer divides 0

Published on 13 Apr 2026 - 16:55

68

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Let $\alpha \neq \beta$ be the roots of $x^2 + ax + b \in\Bbb R[x]$. Prove $\exists c \in \Bbb R$ such that $\alpha-\beta=c$ or $\alpha-\beta=ci$.

Published on 17 Apr 2026 - 6:59

214

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All Gaussians are affine transformations of the standard Gaussian original proof

Published on 14 Apr 2026 - 4:27

93

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Order of double coset with group actions

Published on 14 Apr 2026 - 2:08

117

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A Half Partition of Borel Sets will Give Half the Borel Measure

Published on 15 Apr 2026 - 13:12

53

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Exercise 5, Section 6.4 of Hoffman’s Linear Algebra

Published on 10 Apr 2026 - 10:40

List Question

Is there any better way of evaluating the summation

Finding an alternative nicer method to evaluate the summation

Induction proof that the $n$-sphere $S^{n}$ is connected

Suppose $\ a,b\in\mathbb{Q}^+.\ $ Then $\ \exists\ c,d,k\in\mathbb{Z}^+,\ $ such that $\ a = \frac{c}{k},\ b = \frac{d}{k}\ $ and $\ \gcd(c,d,k)=1.$

Need verification (and an alternative, if that's possible) for proof on generalization of direct sum

Any hints to shortly prove that $f(x) = (x^2-1)^2 \cosh2 x-(x^2+1)^2$ crosses the $x$ axis only once?

Can this intuitive explanation of the Change of Variable Theorem be turned into a proof?

Equation of a plane in normal form

A Countable Union of Closed Set that is Actually Closed

Prove that 1 divides every integer, and that every integer divides 0

Let $\alpha \neq \beta$ be the roots of $x^2 + ax + b \in\Bbb R[x]$. Prove $\exists c \in \Bbb R$ such that $\alpha-\beta=c$ or $\alpha-\beta=ci$.

All Gaussians are affine transformations of the standard Gaussian original proof

Order of double coset with group actions

A Half Partition of Borel Sets will Give Half the Borel Measure

Exercise 5, Section 6.4 of Hoffman’s Linear Algebra

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