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Questions tagged [proof-verification]

For questions concerning a specific proof or a specific solution, asking for verification, identifying errors, suggestions for improvement, etc. (You should not use this tag if the question does not contain a proposed proof/solution.)

For questions concerning a specific proof (or a proof sketch) or a solution to some problem; asking a question with this tag indicates one would like answers to respond broadly as to the following:

  • Verification of the proof/solution;
  • Identifying errors in the proof/solution;
  • Suggestions for improving the proof/solution;
  • Alternative approaches.

Also, consider the related tags and .

22798 questions
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Convergence of integral, that is absolutely convergent, proof

Can you think of any proof on convergence of improper integral, that is absolutely convergent? It is so obvious, that I really don't know where to start. Triangle inequality gives us $$\Bigg|\int_a^{\infty}f(x)\ dx\Bigg| < \int_a^{\infty}|f(x)|\…
Jules
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Regularity of Wavelets

In theorem 2.9.2, where we are discussing the Regularity of wavelets. The proof begins by showing the uniform boundedness of the function before the proof of holder inequality in two parts one for small and other for large scale.Now my problem is…
Andres
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Prove: $x^n=0 \to x=0$

I must prove the following: Prop. : let $x \in \Bbb{R}, n \in \Bbb{N}-\{0\}$ then $$x^n=0 \to x=0$$ Proof : by contradiction I have $x \neq 0$, by trichotomy one of the following holds $x <0 $ $x >0$ 1) if $x >0$ then $x^n>0$ therefore $x^n\geq…
mle
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Correctness of Proof by Refutation

I am trying to solve the following by proof by refutation: A or B 1. NOT A or I 2. NOT B or T 3. NOT I 4. NOT T 5. Where the goal is to prove a contradiction. My approach has been: NOT A 6. [2+4] NOT B 7. [3+5] CONTRADICTION 8. [1+6+7] By the…
MrD
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if $a|b, (a,b)=a$

I want to show that this is true. Here's my approach. Let $(a,b)=d$ be the greatest common divisor of $a$ and $b$. Since $a|b,$ there exists an integer $k$ such that $b=ak$ Thus $(a,ak)=d$. Since $(a,ak)=d$, there exist integers $s,t$ such…
Lalaloopsy
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Disproving 0 as a dividend

Prove each of the following statements. (a) For all $b \in \mathbb{Z}$ if for all $k \in \mathbb{N}$, $b \not\mid k$, then $b = 0$. By hypothesis: $b \not\mid k \implies b\ell \neq k, \ell \in \mathbb{Z}$. Note: $b \in \mathbb{Z} \wedge \ell…
Guest
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Proof Verification

Prove that if $f$ and $g$ be monotone functions on $\Bbb R$ such that $f$ is continuous and $g(x) = f(x)$ for all rational numbers $x$, then $g$ is also continuous on R. Solution: Assume $f$ and $g$ are monotone increasing. Suppose that $g$ is not…
123
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Sylvester Gallai Problem

Recently I came through a book of Arthur Engel which mentioned a problem called Sylvester Problem which states that- A finite set $S$ of $n$ points in the Euclidean Plane has the property that any line through two of them passes through a third.…
William Hilbert
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Proof: $\sum_{i=1}^pE_i \doteq \bigoplus_{i=1}^p E_i \leftrightarrow \forall i\in \{1,...,p\}(E_i \cap \sum_{t \in \{1,...,p\}-\{i\}}E_t=\{0\})$

I am using the following definition: Def.: let $E_1,...,E_p$ $p$-vector subspaces of $V$, $E_1+E_2+...+E_p$ is direct sum, $E_1+E_2+...+E_p \doteq E_1\oplus E_2 \oplus ... \oplus E_p$, if $$\forall e_1 \in E, e_2 \in E_2,...,e_p \in E_P…
mle
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(solved)Proof by contradiction: Let $n > 1$ be an integer. if $n$ is a perfect square, then $n+3$ cannot be a perfect square.

My Work so far: Contradiction: Assume that both $n$ and $n + 3$ are perfect squares. $n = a^2,\ n+3 = b^2$ Now, $3 = (n+3) - n = b^2 - a^2 = (b+a)*(b-a)$ so we assume that $b+a = 3$ and $b-a=1$ which means $a = 3-b $ so $b+b-1=3 \Rightarrow 2b=4…
Jaideng123
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Is the prove correct for: If both ab and a + b are even then both a and b are even

Show: If both $ab$ and $a + b$ are even, then both $a$ and $b$ are even Proof: Assume both $ab$ and $a + b$ are even but both $a$ and $b$ are not even Case1: one is odd $a=2m+1$, $b=2n$ Hence $a+b = (2m+1) + 2n = 2(m+n) + 1$ Case2: both are…
Abdul Rafae
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How to prove that, for each $n\in \mathbb N$

$$ \frac{x^{n+1}-1}{x-1} = 1 + x + x^2 + \dots + x^n $$ where $x\neq 1$, $x\in \mathbb R$. I am really tired to prove that questions. I can not understand any one. Please help me.....How to prove that, for each $n\in \mathbb N$ (using Mathematical…
user111554
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Angle proof question.

Hi, I just want to know if my proof seems ok. So we can begin with : 1 degrees = 1+1/9 grads we multiply by x to generalize x degrees= x+x/9 grads now, we take x degrees and multiply it by 60 minutes to know how many minutes it makes.We also do the…
user108343
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3 answers

Prove If $a^3>a$ then $a^5>a$

Prove If $a^3>a$ then $a^5>a$ Here was my go at it: Assume $a^3>a$. Then $$a^3>a\Rightarrow a^3-a>0\Rightarrow a(a+1)(a-1)>0$$ Solving this inequality gives the truth set $\{x\in\mathbb{R}:-11\}$. Then solving the inequality $a^5>a$ I…
dserver
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Existence of isomorphism between $\mathbb{Z}/(p)$ and some finite group $G.$

Let $G$ be a group with $|G|>1.$ Suppose $G$ and $\{e_G\}$are only subgroups of $G.$ Then, there exists $p \in \mathbb{P}$ such that $G \cong \mathbb{Z}/(p).$ May I know if my proof is correct? Thank you for your attention. Proof: Let $|G|= p \in…
Alexy Vincenzo
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