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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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Is the following proof rigorous? How could I improve or correct it?

Proof that $\sqrt{2}$ is irrational using the unique prime factorization theorem. My proof: Assume for the purpose of contradiction that $\sqrt{2}$ is rational. By the unique prime fact. the., we now that $\sqrt{2} = x^y $ where $x$ is a prime and…
Joel
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Proof infinity=1 IDK is there an error?[Solved]

Can anyone find the error in this? Or is this just another divergent series?
user230776
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$gcd(ka,kb) = k \times gcd(a,b)$

I know this this a duplicate, but I would like to know if my solution is fine. $gcd(ka,kb) = (ka)f + (kb)j$ for some $k,a,b,j,f \in Z$ since $gcd(f,j) = 1$ then we can write; $(ka)f + (kb)j = k(af + bj) = gcd(a,b) \times k$. Is this correct? if not…
user197848
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Prove $\sigma(2^{k-1})=2^k-1$

Is there any way to prove this? rather than just plugging in numbers? It's related to Mersenne Primes for anyone interested. I only wanna know the proof to the above statement. Thank you.
amin
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Prove that if $p$ is a prime number and $p\neq3$, then $3$ divides $p^2+2$

Can someone help me with this? I'm not sure how to approach it.. anything would be helpful! Prove that if $p$ is a prime number and $p\neq 3$, then $3$ divides $p^2+2$ In my textbook the hint it gives states that: when $p$ is divided by $3$, the…
user87654321
  • 11
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Greatest common divisor proof.

Show that $c|a$ and $c|b$ iff $c|gcd(a,b)$ I am only going to show that the if part is true and i have the solution to this proof just i found the if part of the proof dissatisfying. since c|a, c|b and $c \le gcd(a,b)$ it follows that there exists…
user197848
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Just some integral confirmation.

I have a first order differential to solve; $$\frac{dr}{d\theta}=\cot\theta \cdot r$$ I have solved it to get this in explicit form; $r = B\sin\theta$ where $B$ is an arbitrary constant. I just like for someone to tell me whether i am correct or not…
user197848
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Groups: proof-verification

Assuming $(G,*)$ is an non-abelian group and $a,b\in G$. I have these two equations: $a*x=b$ and $y*a=b$. First I had to prove, that both of the equations are uniquely solvable ($x_1=x_2$ and $y_1=y_2$), which I did. But now I need to find an…
Arthur
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Two example statements meant to demonstrate the importance of quantifier order don't appear to do so

In a book1 I have encountered the following: To check your understanding of [the importance of quantifier order], consider the following two statements. One is true, and the other is false. Which is which? $$ \exists y > 0\ \text{such that}\…
user211145
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Prove every integral ideal $J$ is identical with $\Bbb{J}_m$ for some $m$.

Prove every integral ideal $J$ is identical with $\Bbb{J}_m$ for some $m$. Suppose $J \neq \{0\} = \Bbb{J}_0$. By the least integer principle, there exists an $m \in J$ such that $rm \in J$ in $r \in \Bbb{Z}$. But then if $J \neq \Bbb{J}_{m_0}$ for…
Don Larynx
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Proving inverse implication by conversion

I have proven logically that the inverse of an implication is true if and only if the converse of said implication is true (as shown below). proposition 1: k has same parity as 2j proposition 2: k is even implication: If k is even, then k has the…
Jim22150
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Gödel's Ontological Argument - Why Are Positive Properties Possible?

I'm not sure if I'm allowed to post links, but I found a copy of Gödel's actual ontological argument published by professor Elke Brendel at Universitat Bonn, and can usually find it through Google. There are four theorems in the proof, and I think…
theboombody
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Verification of theorem

While playing with numbers, I discovered a relationship which I would like to verify here. $a^p\mod p=a \mod p$ when $p$ is prime Proof: If $c$ is prime number, then; $a^c\mod{p}=\mod(\mod (b^c)+\mod(d^c))$ where $b+d=a,$ By splitting $b$ and $c$…
Curious
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Integral of a complex number showing 1=2?

$$\int z \,dz=\dfrac{z^2}{2}$$ $$z=a+bi\implies \int (a+bi) \,dz=\int z \, dz$$ $$a(a+bi)+bi(a+bi)=(a+bi)^2=\dfrac{z^2}{2}=\dfrac{(a+bi)^2}{2}$$ $$ 2(a+bi)^2=(a+bi)^2$$ Assume $z \neq 0$: $$1=2$$ Where is the fallacy?
Teoc
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System with two quadratic equations

Respected All. I am unable to find out what's so wrong in the following. Please help me. It is given that $t$ is a common root of the following two equations given by \begin{align} &x^2-bx+d=0 \tag{1}\\ &ax^2-cx+e=0 \tag{2} \end{align} where…
KON3
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