Questions tagged [solution-verification]
For posts looking for feedback or verification of a proposed solution. "Is this proof correct?" or "where is the mistake?" 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 duplication.
23,113 questions
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Another approach to Nullstellensatz?
Proposition: Suppose $k$ is an algebraically closed field and $A$ is a finitely generated $k$-algebra that is also an integral domain. Then there exists a (unital) $k$-algebra homomorphism $\varphi:A\...
- 71
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Does this proof work for proving if $(a_n)$ converges to $L$ then there are only finitely many terms with $a_n=M,$ $M$ not equal to $L?$ [closed]
Question: Let $(a_n)_{n\in\Bbb{N}}$ be a convergent sequence, limit $L$ and let $M$ be some real number with $M\ne{L}$. Show that the set $$S=\{n\in\Bbb{N}:a_n=M\}$$ is bounded above.
My proof:
The ...
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Isomorphism from Zn to Zn [closed]
Ring Isomorphisms from Zn to Zn
Question:
Find all ring isomorphisms from Zn to Zn.
Solution:
Let f: Zn → Zn be a ring isomorphism.
Then, f(1) = a.
Assume gcd(a, n) = k.
If k > 1, ...
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Let $X$ and $Y$ be two events such that $P(X | Y)=\frac12$ and $P(Y | X)=\frac13$ then which of the following options is correct?
(Only one option is correct)
Question:
Let $X$ and $Y$ be two events such that $P(X | Y)=\frac12$ and $P(Y | X)=\frac13$ then which of the following options is correct?
A) X and Y can be exclusive ...
- 10.6k
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A Standard Contour Integral?
Suppose we want to evaluate the integral $I := \displaystyle \int_{\mathbb{R} > 0} \dfrac{x^\alpha}{(1+x^2)^2} \ \mathrm{d}x$, where $-1 < \alpha < 3$. For $\alpha \neq 1$, it is known that ...
- 2,227
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Number of similarity classes of $3 \times 3$ complex matrices annihilated by the polynomial $(1-x)(1-x^2)\cdots(1-x^9)$
I want to find the number of similarity classes of $3 \times 3$ complex matrices annihilated by the polynomial $(1-x)(1-x^2)\cdots(1-x^9)$.
From an annihilating polynomial, we can determine the ...
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Counting zeros in the right-half plane (exponential polynomial)
Consider the complex polynomial
$$
h(\lambda)=\lambda^2-(\alpha+\beta\lambda)e^{-\lambda}+\gamma+\delta\lambda, \quad \lambda\in\mathbb{C}, \,\, \alpha,\beta,\gamma,\delta\in\mathbb{R},
$$
where $\...
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If $\mathfrak X$ is a collection of subgroups then $\bigcup\mathfrak X$ is a subgroup iff $\mathfrak X$ is a inclusive chain.
Let be $(G,\ast,e)$ a group so that let be $\mathfrak X$ a collection of subgroup of $(G,\ast,e)$.
If $\mathfrak X$ is an inclusive chain then it is not hard to show that $\bigcup\mathfrak X$ is a ...
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Is this approach to proving the multilinearity of the determinant valid (using Smith normal form)?
I'm working on an exercise in linear algebra involving the multilinearity of the determinant. The task is:
Let $𝐾$ be a field. Consider the determinant as a function:
\begin{align}
&\det : K^n \...
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Find the number of solutions of $x^3-x^2(1+\sin x)+x(\sin x-\cos x)+\cos x=0$, where $x\in(-\frac{\pi}2,\frac{\pi}2)$
Find the number of solutions of $x^3-x^2(1+\sin x)+x(\sin x-\cos x)+\cos x=0$, where $x\in(-\frac{\pi}2,\frac{\pi}2)$
My Attempt:
If I take $\sin x=0$ then $\cos x=1$, thus the equation becomes $$x^3-...
- 10.6k
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Morphism between finite abelian groups $A$ and $A\oplus B$ in $\textbf{FinAb}$
Denote by $\textbf{FinAb}$ the category of finite abelian groups. Let $A,B\in\textbf{FinAb}$.
Is there a morphism between $A$ and $A\oplus B$ in $\textbf{FinAb}$, i.e., is there an injective ...
- 1,363
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Break self-intersecting closed curve into several simple closed curves
Intuitively, I can say that we can break self-intersecting curves who intersects itself finitely many times into several simple closed curves in $\mathbb{R}^2$. Like this:
I was trying to say that ...
- 115
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identity theorem proof in Stein and Shakarchi
I am reading the proof of the identity theorem (if two holomorphic functions agree on a non-empty open set, then they coincide), or its preliminary, which I upload here.
My concern is the line where ...
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Forcing to add a Kurepa tree with many branches
$\newcommand{\dom}{\operatorname{dom}}$$\newcommand{\ran}{\operatorname{ran}}$A Kurepa tree is a tree with height $\omega_1$ that has countable levels and at least $\omega_2$ branches. There is a ...
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Is the following proof for the dimension of the sum of three vector spaces valid? [closed]
Let $V_1, V_2$ and $V_3$ be subspaces of a finite dimensional vector space, then
$$
\dim(V_1 + V_2 + V_3) = \dim(V_1) + \dim(V_2) - \dim(V_1 \cap V_2) + \dim(V_3) - \dim((V_1 + V_2) \cap V_3)
$$
Proof:...
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