# Tagged Questions

This tag is for readers who ask for explanation and clarification of some steps of a particular proof.

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### Reverse Proof for Eucildean Algorithm [on hold]

For each part, find integers $m$, $n$ such that $\gcd(am, b) = am + bn$. $$\gcd(7, 2) \\ \gcd(52, 16) \\ \gcd(1492, 2014) \\ \gcd(528740, 615846)$$
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### Proof of closed,continuous , surjective image of a *Normal* space is normal.

$$p:X\rightarrow Y$$ is closed,continuous,surjective map. $X$ is normal . To prove that $Y$ is also normal. So I use this result : A space $X$ is normal iff for any closed set ...
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### Confusion regarding a (possibly) informal use of “continuously” in Artin's section about $SO_3$

This is regarding Artin's proof of the following statement in his Algebra: Let $M$ be the matrix in $SO_3$ that represents the rotation $\rho_{(u,\alpha)}$. Let $B$ be another element of $SO_3$, ...
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### Integration of motion using resistance and gravity.

I'm having trouble with a high school mathematics question. An object of mass $1kg$ falls from rest in a medium in which the resistance to motion is given by $r=kv^2$, where $k$ is a constant and $v$ ...
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### One statement about definite integrals implying an another.

Could anyone please explain me the following statements : "$$\int_{0}^{\theta}g(y)\frac{2n}{\theta^{2n}}y^{2n-1} dy=0$$ for all $\theta$ implies $$g(\theta)\frac{2n}{\theta^{2n}}\theta^{2n-1}=0$$ for ...
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### Help with Proposition $2.3.3$ from Elem. Differential Geometry by Pressley

Why can we have $\mathbf v \cdot \mathbf N =d$? Why is $\mathbf v \cdot \mathbf N =d$ a plane? Where did $\gamma \cdot \mathbf N=d$ come from? Why can we do this?
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### Proof of (1+a)^n

I've just started going through some very basic analysis and was working through an attempt at a proof that $(1+a)^n \geq 1 + na + \frac{1}{2} n (n-1)a^2$ I got about half way through, and found I ...
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### What is meant by "equating the coefficients of 1, x, and $x^2$ gives a set of linear equations?

The textbook I am reading shows an example problem: Problem: Show that {$1 + x, 3x + x^2, 2 + x - x^2$} is independent in $P_2$. Where $P_2$ is the set of all polynomials. Solution: Suppose a ...
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### $4ab-2-5b=0$ have no solution

$a,b$ are natural numbers . Show that $4ab-2-5b=0$ has no solution . By contradiction : $b(4a-5)=2$ So $4a-5=${1,2} which gives $a\in\mathbb{Q}$ ( contradiction) So the equation has no solution ! ...
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I am unable to understand the solution to this question: "At your subway station, you notice that of the two trains running in opposite directions which are supposed to arrive with the same frequency, ...
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### Impartiality axiom in Terry Tao's Arrow's Theorem proof

The short expository paper is here. On page 2, The notion of a quorum is well-defined; it is not possible for such a group to be able to force a vote some of the time and not at other times ...
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### Some questions about generic points and regular points on a scheme

Recently, I've been reading this paper about Brauer groups. I am not sophisticated with algebraic geometry, and got some confusions about the proof of lemma 3. These questions may be naive for ...
### Computing $\int \sin^n ax \, dx$
I need to compute the following integral. Looking on an integral table I've found that the closed form of this integral is equal to:  \int \sin^n ax \, dx = -\frac 1 a \cos ax\ _2F_1 \left[ ...
The following is from this paper that discusses polynomials and classic number theory functions. The proof of theorem 1.3 has a final statement saying that $R$ must be null because we arrive at ...