Questions tagged [solution-verification]

For posts looking for feedback or verification of a proposed solution. "Is my 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.

This tag should be used when you have a proposed solution to a problem and have specific concerns or doubts about the validity of that solution. A question with this tag should include an explanation for why the argument presented is not convincing enough. Further discussion on using this tag can be found in the Mathematics Meta questions (1) and (2).

Answers to questions tagged look first and foremost to check that the solution is right, and to comment upon the approach taken by the author of the question. If the proposed solution is wrong, a good answer would explain where or how mistakes were made, and possibly give or sketch a correct solution instead.

If the proposed solution is correct, an answer would ideally provide further evidence to back the answerer's opinion. These could include a clearer rewriting of the given argument, alternative arguments, generalizations of the proven result, or careful consideration of unexpected subtle points. Users looking to write answers can find further discussion in this Mathematics Meta post.

21426 questions
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Prove that the normalizing constant of the continous categorical distribution is positive

Problem statement Given a vector $\mathbf{x} \in \mathbb{R}^{K}$, where $x_{i} \neq x_{j}, \forall i \neq j$. Prove that: \begin{equation} \sum_{k=1}^{K} \frac{\exp(x_{k})}{\prod_{i \neq k} (x_{k} - x_{i})} \ge 0. \end{equation} If it is wrong, I…
Cuong
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Proof of $(ab)^{-1} = a^{-1}b^{-1}$

I wonder if you would consider this proof of my hypothesis of $(ab)^{-1} = a^{-1}b^{-1}$ with $a,b\ne0$ correct. By definition of the inverse of $ab$: $$(ab)^{-1}(ab)=1$$ Multiplying the equation with $a^{-1}$ and $b^{-1}$ gives…
Binomi
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Is there a universal math proof verification program than can verify every finite purported math proof?

For some axiom systems, we can verify candidate proofs. For example Mizar. Is there a universal language we can write proofs in, so that the axioms are included in the proof, along with every single step in complete detail, so that some universal…
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Prove $\sin x < x < \tan x$ for $0 < x < \pi/2$ algebraically

I know there are some proofs showing that, for $0 < x < \pi/2$: $\sin x < x < \tan x $ with the use of the unit circle, however, can I prove this algebraically in some way as well?
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How to prove a hard inverse trigonometry mathematical induction

$\arctan\left(\frac{1}{2\left(1\right)^{2}}\right)+\arctan\left(\frac{1}{2\left(2\right)^{2}}\right)+\arctan\left(\frac{1}{2\left(3\right)^{2}}\right)+...+\arctan\left(\frac{1}{2\left(n\right)^{2}}\right)=\frac{\pi}{4}-\arctan\left(\frac{1}{2n+1}\rig…
user71207
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Proving equality of two expressions

can anybody help on proving equality of those two expressions? Actually, those are different forms of Gassmann equation, the first one is considered to be the main form. $$K_{sat}=K_{dr}+\frac{K_f\alpha^2}{\Phi…
ingenue
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how can I prove this equation using Induction?

How can I prove this mathematical by induction? $(2) = (+1)^2 − (−1)^2$ and using this relation F(2n+1)=F(n+1)^2+F(n)^2
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Can I prove " For each real numbers can be expressed as sum of two irrational numbers." like this?

Can I prove it like this? Proof Case 1 Suppose $x=\sqrt2$ . Choose $y=\sqrt2-\sqrt3$ , $z=\sqrt3$ consider $y+z=(\sqrt2-\sqrt3)+\sqrt3=\sqrt2=x$ Case 2 Suppose $x\in\mathbb{R}$-{$\sqrt2$}. Choose $y=x-\sqrt2$, $z=\sqrt2$ consider…
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Is this proof that the sum of two natural number is a natural number?

Introduction I saw a video of a guy talking about proving that a even number squared is still even. It was something like this: Let n be a natural/whole number, and 2n defines all even numbers: 2n * 2n = 4n² = 2(2n²) So, 2(2n²) is an even…
user784856
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Proving a property of concave functions

Let $f$ be a concave function. Then, by definition, for any $\alpha \in [0,1]$ \begin{equation} f(\alpha x + (1-\alpha) y) \geq \alpha f(x) + (1-\alpha) f(y) \end{equation} Is there a way to prove that \begin{equation} f(x) + f(y) \leq f(\alpha x…
fennel
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If $a+\sqrt{a}=b+\sqrt{b}$ is $a=b$?

If $a+\sqrt{a}=b+\sqrt{b}$, does this automatically mean that $a=b$? I first tried to square both sides but that seemed to get me nowhere. $$a-b=\sqrt{b}-\sqrt{a}$$ Can we just conclude that $a$ has to be equal to $b$ to make this expression to be…
John Rawls
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If $m$ and $n$ are positive integers, prove that $\sqrt[m]{n}$ is either a positive integer or irrational.

If $m$ and $n$ are positive integers, prove that $\sqrt[m]{n}$ is either a positive integer or irrational. I just need someone to verify my proof, which is as follows. Clearly, if $n = k^m$ for some positive integer $k$, then $\sqrt[m]{n}$ is a…
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Prove that if $a+b$ is an irrational number, then at least one of $a$ or $b$ is irrational.

I came across this question in a book. I tried proving the condition as the following: Suppose that a and b are rational. Clearly the sum of $a$ and $b$ is rational, which contradicts the condition, which is that $a+b$ is irrational. Therefore at…
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Proof Question: Set $\theta = \{((x^2,y),(y,2x,x-y)): x,y \in \mathbb{Z}\}$ a function? What is domain, range, codomain?

Set $\theta = \{((x^2,y),(y,2x,x-y)): x,y \in \mathbb{Z}\}$ a function? What is domain, range, codomain? Domain: set of $(x^2,y)$ for $x,y \in \mathbb{Z}$ Range: set of $(y,2x,x-y)$ for $x,y \in\mathbb{Z}$ and the codomain is the same as the…
EM4
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Can this be accepted as a proof of the question.

Let $a,b\in+\mathbb Z$ such that $\dfrac{a^2+b^2}{ab+1}=k.$ Prove that $k$ is the square of an integer when $$a^2+b^2$$ is divisible by $ab+1$. Soln. For $k$ to be a perfect square, $\dfrac{a^2 + b^2}{1+ab}$ must be in the form…
Daniel
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