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.
46,206 questions
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Property Preserved By Toplinear Isomorphisms.
Suppose $V$ is a topological vector space over $\mathbb{R}$ relative to vector addition $\boxplus$, left scalar multiplication $\boxdot$, and the topology $\mathcal{T}$. Suppose $W$ is a topological ...
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4 votes
1 answer
164 views
Arrangements of 10 Balls Chosen from Red and Blue, Where Every Blue Ball Has a Blue Neighbor(need pure combinatorics solution)
Question Consider a linear arrangement of $10$ balls selected from an infinite supply of blue and red balls. Determine the total number of distinct arrangements that satisfy the following condition: ...
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2 votes
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Every k-fold cover of the real line by intervals can be decomposed into k distinct covers.
A k-fold cover of the real line is a family of sets such that each point is contained inside atleast k sets in the family. I am trying to prove the following fact which i came across in Yufei Zhao's ...
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Check proof that the determinant of a polynomial matrix commute with evaluation
This is used in one of the many proofs for the Cayley-Hamilton theorem. My professor noted that this should be proved. However, the proof of this fact is rather straightforward, no? Is the proof I ...
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The quadratic equation $x^2 - (c+3)x + 9 = 0$ has real roots $x_1$ and $x_2$. If $x_1 < -2$ and $x_2 < -2$, find value of $c$.
The quadratic equation $x^2 - (c+3)x + 9 = 0$ has real roots $x_1$ and $x_2$. If $x_1 < -2$ and $x_2 < -2$, then the value of $c$ is ... I try: Since there are two real root then \begin{align} ...
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Is using determinants like this for vector algebra standard?
It is known that, $$ \nabla \cdot (\mathbf{A} \times \mathbf{B}) = \mathbf{B} \cdot (\nabla \times \mathbf{A}) - \mathbf{A} \cdot (\nabla \times \mathbf{B}) $$ The straightforward way to prove this ...
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1 vote
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Is a compact hypersurface in euclidean space orientable? [closed]
I'm trying to prove this exercise from G&P book, but I don't know if I'm right in my sketch: here it follows By the smooth Jordan--Brouwer Separation Theorem, $\mathbb{R}^n \setminus \Sigma$ has ...
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-1 votes
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Minimal ε–Index Theorem for Convergent Sequences [closed]
Osamah Banat's Theorem and Algorithm for Minimal ε–Index of Convergent Sequences This theorem presents a method to determine the minimal ε–index for any real sequence converging to a limit L. The ε–...
