# 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.

21,858 questions
Filter by
Sorted by
Tagged with
114 views

### Proof of Linear-Algebra (matrices). [duplicate]

Prove that \begin{align} \begin{pmatrix} \lambda & 1\\ 0 & \lambda \end{pmatrix}^n &= \begin{pmatrix} \lambda^{n} & n\lambda ^{n-1}\\ 0 & \lambda^{n} \end{pmatrix} . \end{align} ...
• 49
217 views

45 views

### Existence of certain function satisfying certain conditions

I want to show that there does not exist $f ∈ C([0, 1], R)$ satisfying the following two conditions: (i) $\int_{0}^{1} f(x) dx = 1$; (ii) $\lim_{n\to\infty} \int_{0}^{1}f(x)^n dx = 0.$ Suppose there ...
• 150
1 vote
38 views

1 vote
35 views

• 155
1 vote
80 views

### $f:A\subseteq \mathbb{R}\to \mathbb{R}^2$ maps closed sets to closed sets.

Can you take a look at my proof, please? Let $f:A\subseteq\mathbb{R}\to \mathbb{R}^2$ given by $f(x)=(x,x^2)$ where $A$ is a closed set and $f$ is continuous in $A$. Show that $f$ maps closed sets to ...
• 565
46 views

### Proof the number of nodes in a full binary tree +1 is equal to the double of the leafs [closed]

This is a class problem from the book https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-spring-2015/resources/mit6_042js15_textbook/ Page 191, I believe I have done it correctly but ...
1 vote
22 views

### Inequation regarding the relationship between |V(G)∣ and the girth of a 3-connected graph

(Dis)prove the following inequation: |V(G)∣ ≥ 2 g(G) - 2 G is a 3-connected Graph g(G) is the length of the shortest cycle in G I had some approaches to the problem but the most promising was: Let ...
57 views

• 23
1 vote
41 views

### Proof of factor theorem regarding polynomials

Division of polynomials: Let $f$ and $g$ be polynomials with $g(x)\neq 0$. Then there exist unique polynomials $q$ and $r$ such that $r=0$ or $\deg r<\deg g$, and $f(x)=q(x)g(x)+r(x)$. I want to ...
62 views

• 141
54 views

### Wrong proof of Inverse function theorem

Is there anything wrong in my attempt to prove the following section of Inverse function theorem by following: The section I try to prove: Let $f:U\subseteq \mathbb{R}^n\to \mathbb{R}^m$ be ...
• 449
61 views

### Proof that the supremum of a continuous function is part of the range of that function

I'm following the textbook "Calculus" By Spivak. Currently, I'm reading a proof given for the following theorem: "If $f$ is continuous on $[a,b]$ then there exists an $x^*\in[a,b]$ such ...
• 273
33 views

### Proof of uniform convergence in $[a,\infty)$ but not $[0, \infty)$

Let $f_n(x)=\frac{x}{(1+x)^n}$. I need to prove that $f(x)=\displaystyle \sum_{n=1}^{\infty}f_n(x)$ is uniformly convergent in $[a,\infty), \forall a>0$ but not uniformly convergent in $[0,\infty)$....
• 1,009
33 views

• 1,465
26 views

### Number of bounded and unbounded components of nonsingular real algebraic curve $y^2 - p(x)$

I would like to know if someone can kindly verify my solution to Problem 22.2 from MIT's online course on geometry and topology in the plane. Let $C = \{(x,y) \in \mathbb{R}^2 : f(x,y) = 0\}$ be a ...
• 577
41 views

• 413
1 vote
46 views

### Intersection of generalized eigenspaces is trivial (proof validation)

Does the following proof work for showing that the intersection of generalized eigenspaces is trivial? Let $A$ be some $n \times n$ matrix with eigenvalues $\mu,\lambda$ where $\mu\neq \lambda$. The ...
• 55
### Probability that before player $X$ throws a $6$, player $Y$ throws what player $X$ threw in the previous throw. Solution verification.
Two players ($X$ and $Y$) take turns rolling the dice. Player $X$ starts the game. Calculate the probability that before player $X$ throws a $6$, player $Y$ throws what player $X$ threw in the ...
### A criterion for proving that an algebraic extension $E \subset F$ of fields is normal.
Let $K \subset F$ be fields such that $F$ is an algebraic extension of $K$, if for all elements $\alpha \in F$ there is a field $K \subset E \subset F$ such that $\alpha \in E$ and $E$ is normal over \$...