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.
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Show that $w\in W$ if and only if $w\wedge w_1\wedge\cdots\wedge w_k = 0$ in $\wedge^{k+1}V$
Let $w_1,\dots,w_k$ be linearly independent and $W=\mathrm{span}\{w_1,\dots,w_k\}$.
If $w\in W,ドル then
$$
w = a_1 w_1 + \cdots + a_k w_k
$$
for some scalars $a_i,ドル then $\{w,w_1,\dots,w_k\}$ is l.d. ...
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Property Preserved By Toplinear Isomorphisms.
Suppose $V$ is a topological vector space over $\mathbb{R}$ relative to vector addition $\boxplus,ドル left scalar multiplication $\boxdot,ドル and the topology $\mathcal{T}$. Suppose $W$ is a topological ...
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$f(0)=1,ドル $f(x) \ge 0 \ge f'(x),ドル $f''(x)\le f(x)$ for $x\ge 0$
Problem
Let $f$ be a twice differentiable function on the open interval $(-1,1)$ such that $f(0)=1$. Suppose $f$ also satisfies $f(x) \ge 0, f'(x) \le 0$ and $f''(x) \le f(x),ドル for all $x\ge 0$. Show ...
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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ドル$ 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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Is the isomorphism $(G/N_1)/(N_2/N_1)\cong G/N_2$ in the third isomorphism theorem actually an equality?
I tried to understand the concept that, for a group $G$ and two normal subgroups $N_1,N_2$ with $N_1\subseteq N_2$ it holds that
$$(G/N_1)/(N_2/N_1)\cong G/N_2,$$
but my following reasoning seems to ...
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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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How $\min(x,y)$ works in reasoning
I came across this proof from a reliable book, showing that the set $X=\lbrace x \in \mathbb{R} \mid x \gt 0 \text{ and }\:x^2\leq2\rbrace$ has a supremum $a$ which verifies $a^2=2$. We have proven ...
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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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Prob. 7, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: Is $\overline{S_\Omega}$ first-countable? second-countable? separable? Lindelof?
Here is Prob. 7, Sec. 30, in the book Topology by James R. Munkres, 2nd edition:
Which of our four countability axioms does $S_\Omega$ satisfy? What about $\overline{S_\Omega}$?
Our four ...
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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,ドル 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,ドル then the value of $c$ is ...
I try:
Since there are two real root then
\begin{align}
...
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I want to verify if my approximation of the equation is correct [closed]
I want to verify if my approximation of the equation is correct.
The original equation is:
$1ドル - 3(1-X)^{2/3} + 2(1-X) = \tau$$
where:
$X$: fraction reacted (0ドル \leq X \leq 1$)
$\tau = k_D t/R^2$: ...
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Is using determinants like this for vector algebra standard?
It is known that, $$
\nabla \cdot (\mathbf{A} \times \mathbf{B}) = \mathbf{B} \cdot (\nabla \times \mathbf{A}) - \mathbf{A} \cdot (\nabla \times \mathbf{B})
$$
The straightforward way to prove this ...
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Quotienting the real line by conjugate elements of real affine group $\mathrm{Aff}(\Bbb R)$
Consider the real affine group $\mathrm{Aff}(\mathbb{R})$ and elements $p,q,z\in \mathrm{Aff}(\mathbb{R})$ such that $$p=z^{-1}q z.$$ Consequently, $p,q$ are by definition conjugate. Assume that $\...
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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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uniqueness of a map and universal property
I am trying to prove the following statement:
For any two non-empty sets $X,Y,ドル an equivalence relation $E$ on $X,ドル and an injective function $h:X/E\to Y,ドル show that there exists a unique function $H:...