# Questions tagged [solution-verification]

For posts looking for feedback or verification of a proposed solution. "Is this proof correct?" is too broad or missing context. Instead, the question must identify precisely which step in the proof is in doubt, and why so. This should not be the only tag for a question, and should not be used to circumvent site policies regarding duplicate questions.

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### Can fundamental theorem of algebra for real polynomials be proven without using complex numbers?

Update 24 Nov 2015: It is solved. Please refer to this arXiv paper. For polynomials with real coefficients, I am trying to prove the following version of fundamental theorem of algebra, which avoids ...
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### Theorem 6.17 in Baby Rudin, 3rd ed: $\int_a^b f \,d\alpha = \int_a^b f(x) \alpha^\prime(x) \,dx$

Here is Theorem 6.17 in the book Principles of Mathematical Analysis by Walter Rudin, 3rd edition: Assume $\alpha$ increases monotonically and $\alpha^\prime \in \mathscr{R}$ on $[a, b]$. Let $f$ be ...
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### Erratum for Billingsley’s $\textit{Probability and Measure}$, Problem 32.13

This is a verification request for a counterexample that I think I have found for Problem 32.13 on page 427 in Patrick Billingsley’s Probability and Measure textbook (third edition, but the problem ...
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### A very general method for solving inequalities repaired

Yesterday, I asked a question about a very general method for solving equations I had found here. As it turned out, there were quite some problems with my method and I got a lot of good feedback. ...
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### About Theorem 3.4 Hartshorne: detailed proof.

I propose a detailed version of part of the proof of Theorem 3.14 from Hartshorne's book Algebraic Geometry. The questions are inserted from time to time within the proof. Thanks for your patience. ...
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### Fermat's Last Theorem ($n=4$) using the Gaussian integers

I'm doing the second part of the following exercise in Miles Reid's Undergraduate Commutative Algebra: Exercise 0.18: Prove the cases $n=3$ and $n=4$ of Fermat's last theorem. I would like to know: ...
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### Proof of one-side version of Bennett-Bernstein inequality

I'm going to prove the following: For independent random variables $X_i$, $i \in [m]$ satisfying $X_i-E[X_i] \le b$ for some constant $b > 0$. Let $\bar{X} = \dfrac{1}{m}\sum_{i=1}^m X_i$, we have ...
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### The volume of $k$-parametrised manifolds when $k=1$ or $k=2$ or $k=3$ agrees respectively with the usual intuitive idea of length or area or volume.

James Munkres, at the chapter $22$-th of the text Analysis on Manifolds, gives the following definition. Furthermore, to point out I say that the function $V\left(D\alpha\right)$ corresponds with ...
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### Cotangent complex of dual numbers

Let $k$ be a ring, put $k[\epsilon] := k[t]/(t^2)$. What is the cotangent complex of $k[\epsilon] \to k$? I know $\Omega^1_{k/k[\epsilon]]}$ is going to be zero. But I don't see any way around ...
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### Methods to solve $\int_{0}^{\infty} \frac{\cos\left(kx^n\right)}{x^n + a}\:dx$

Spurred on by this question, I decided to investigate for different functions on the numerator. Here, I went from $\exp(..)$ to $\sin(..) / \cos(..)$. I initially thought I could modify the result ...
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### Is Hilbert's space-filling curve measure preserving?

Say $f_n:[0,1]\to [0,1]^d$ is the $n$-th iteration of a $d$-dimensional Hilbert curve touring its range. Is it true that for any open $S\subset [0,1]^d$, then amount of time $f_n$ spends in $S$ is ...
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### Proof correctness problem

I was watching this talk by Vladimir Voevodsky which was given at the Institute of Advanced Study in 2006. In his talk the first slide he shows has the following written on it: ...
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### Any non-trivial finitely-generated group admits maximal subgroups

I want to solve the following problem from Dummit & Foote's Abstract Algebra: This is exercise involving Zorn's Lemma (see Appendix I) to prove that every nontrivial finitely generated group ...
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### On the centralizers of $n$-cycles and conjugacy in $A_n$

I'd appreciate comments on the validity of these attempted proofs. Thanks. Let $a$ be an $n$-cycle in $S_n$. a) Show that the centralizer of $a$ in $S_n$ is $\langle a \rangle$. b) Assume that $n$ ...
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### Probability of winning a game guessing $k$ random numbers in sequence with optimal strategy

We are playing a game as follows, suppose we have $k$ spaces. One at a time, we will pick $k$ random integers from the range $[1,n]$, without replacement. After selecting a number, we must choose to ...
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