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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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If $f:[0,1] \to \mathbb{R}$ is continuous and $\int^{x}_{0} f = \int^{1}_xf,$ then $f(x) = 0, \forall x\in [0,1].$

If $f:[0,1] \to \mathbb{R}$ is continuous and $\int^{x}_{0} f = \int^{1}_xf,$ then $f(x) = 0, \forall x\in [0,1].$ May I verify if my proof is valid? Thank you:) Proof: $\int^{c}_{0} f = \int^{1}_cf…
Alexy Vincenzo
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Proof: Divisible by 15

I have to proof that $16^m - 1$ is divisible by $15$. Is my following proof correct? $$\begin{align} 16^m - 1=&\frac{16^{m+1}}{16}-1\\ =&\frac{16^{m+1}-16}{16} \\ =&(16^{m+1}-16)\cdot\frac{1}{16}…
gosua
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Proving that $f(x) = x^{1/3}$ is absolutely continuous.

Here is a trial: We will divide our interval into 2 intervals $[-1, 0)$ and $[0,1]$:\ (1) for the interval $[-1, 0)$, our function is increasing on $(-1,0)$ then it is differentiable a.e. on $(-1,0)$ by Lebesgue theorem and its derivative is $f'(x)…
Intuition
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Prove $(R^{-1})^{-1} = R$

The problem is actually pretty simple, but because of the double inverse, I got confused on how to properly write the proof. I just want to make sure that What I wrote is actually valid. proof: (i)Suppose (x,y)$\in (R^{-1})^{-1}.$ Then by the defn…
Jr194
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Proof Verification: Spivak's Calculus, Chapter 1, Problem 1.

Problem: Prove if $ax = a$ for some number $a \neq 0$, then $x=1$. Here is my proof: If $ax=a$, then $a^{-1}ax=a^{-1}a.$ By the existence of multiplicative inverses, $x=1$. Q.E.D Now, I have a feeling that this doesn't show that $x$ HAS to be $1$.…
Athelstan Carlton
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If $a_n \geq 0$ $\forall n \in \mathbb{N}$ and $\sum_{n=1}^ \infty a_n < \infty$, what can be said about $\lim_{k\to\infty}\sum_{n=k}^\infty a_n$?

If $a_n \geq 0$ $\forall n \in \mathbb{N}$ and $\sum_{n=1}^ \infty a_n < \infty$, what can be said about $\lim_{k\to\infty}\sum_{n=k}^\infty a_n$? My claim is that $\lim_{k\to\infty}\sum_{n=k}^\infty a_n = 0$. To see this, first note that for all…
user506873
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Demonstrate that $(x-(\frac{x^2-2}{2*x})\bigr)^2 \gt 2$ for the given conditions.

I am stuck on a proof where I need to demonstrate that $(x-(\frac{x^2-2}{2*x})\bigr)^2 \gt 2$. The proof provides me with the information that $x^2\gt 2$ and $x>0$. I've taken the following steps to simplify the algebra...to the point where I arrive…
S.C.
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Proof of rationality using product lemma

Prove that if $x$ is prime then $x^{3/2}$ is irrational. Is this the correct way to prove this, or is a proof by contradiction preferable? Using the lemma that the product of a nonzero rational number and irrational number is irrational. Proof:…
user707991
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Proving that one can always find a rational number between two real numbers

I recently attempted to prove the following statement: "If $x$ and $y$ are real numbers, with $x \ < \ y$ , there is a rational number $r$ such that $x \ < \ r \ < \ y$" This problem came from a book on proofs that I am currently reading. The author…
S.C.
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Can someone check my proof please for Rudin chapter 4

I want to prove: If $f$ is a continuous mapping of a metric space $X$ into a metric space $Y$, prove that $$f(\overline{E}) \subset \overline{f(E)} $$ for every set $E\subset X$. ($\overline{E}$ denotes the closure of $E$.) If $x$ is in …
mathgeorgie7
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Proof about the sum of integers in the form of 2^n

The question is: Prove that every positive integer can be uniquely expressed as a sum of different numbers, where each number is of the form 2^n for some non-negative integer n. My proof: We see that it works from $1, 2, \dots, 10$ -- assume it…
badrex
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Say $P_0=3,P_1=0$, $P_2=2$ and $P_n= P_{n-2}+P_{n-3}$. Then $p\mid P_p$ if $p$ prime.

Is a proof number 1 on Bogomolny's page valid, namely how does he know that $z$ is an integer? Obviously $r_1,r_2,r_3$ are not an integers.
nonuser
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Trying to prove $\lim_{x \to a} f(x) g(x) = L_1 L_2$

$$\lim_{x \rightarrow a}f(x)=L_1 , \lim_{x\rightarrow a}g(x) = L_2 $$ I'm trying to prove $$\lim_{x \to a} f(x) g(x) = L_1 L_2$$ We have that $$|f(x)g(x)-L_1L_2| = |f(x)g(x)-g(x)L_1+g(x)L_1 -L_1 L_2 |$$ Factoring $g(x)$ and $L_1$ and using triangle…
Melz
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Proof: coherence of risk measure

maybe someone can help me to prove the coherence properties for a risk measure. It's about the coherence of the following risk measure (Entropic Value-at-Risk): $EVaR_\alpha(X):=\underset{z>0}{\inf}\{\frac{1}{z}\ln\left( \frac{M_X(z)}{1-\alpha}…
Keplox
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Solving for an exponential variable that can not be issolated through factorisation.

$$(2^{x}-1)(2^{x}+4)(2^{x}-6)=0$$ My thinking: At least one of the three terms given above should be equal to $0$. But the middle term will never be equal to zero because $2^{x}$ can not be equal to a negative number. Therefore $2^{x} -1=0$ thus…
Carlize Frey
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