Mathematics Stack Exchange
Mathematics Stack Exchange

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.

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Principles of Quantum Mechanics

I have asked this question all over reddit but can't seem to find an answer. I hope it's not the same here. How do you get from equation one to equation two? I have tried so many methods but couldn't get the same answer. I tried $E^{2} = m^{2}c^{4}…
CinemaClips
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subsets as union of intersections between another sets and the space

is this correct? : let $C, A \subseteq X$ then $X= A \cup X\setminus A= \overline{A} \cup \overline{X\setminus A}$ since both sets are closed and open trivially. Hence $C=X \cap C=(\overline{A} \cup \overline{X\setminus A})\cap C= (C\cap…
J.Miller
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Let $n\in\mathbb N$. Prove that if $n^3 − 5n − 10 > 0$, then $ n ≥ 3$

I am currently taking logic and proof techniques course. I encountered this question, and I wonder if my approach is correct or not. Result: Let $n ∈ \mathbb N$. Prove that if $n^3 − 5n − 10 > 0$, then $n ≥ 3$. (From Mathematical Proofs: A…
JackSymBol
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Directed set questions

1.1 Definition. A set $D$ is a directed set if there is an order relation $\prec$ defined on $D$ which satisfies the following: 1.$\prec$ is reflexive 2.$\prec$ is transitive 3.For $x,y\in D,\exists z \in D$ s.t. both $x \prec z$ and $y \prec…
Dazed and Confused
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Proof verification: $\sqrt{p}$ is irrational for prime $p$

I'm trying to prove that $\sqrt{p}$ is irrational for prime $p$. I know how to prove the result when $p = 2$, but I'm not fully certain that every element of my proof generalizes to the case where $p$ is a general prime. In particular, I wrote the…
Cardinality
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Is this a valid way to prove that $\forall x \in \mathbb{R}, \exists y \in \mathbb{R} \ 4x + 3y = 6$?

Attempt: Let $x, y \in \mathbb{R}$ and $4x + 3y = 6$. $$\Rightarrow y = \frac{6 - 4x}{3} = 2 - \frac{4x}{3}.$$ Thus, we have found a real number $y$ for every real number $x$ s.t $4x + 3y = 6$ and conclude that $\forall x \in \mathbb{R}, \exists…
Faith Alone
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Biconditional proof of odd factors and product

EDIT 1: Thanks @coffeemath for pointing out my mistake of defining both m and n in terms of k. They now each have their own respective constants for the Even and Odd forms. EDIT 2: Fixed a typo I'm trying to get my first proof down using…
recur
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Let $f:A\to B$ be a function. Show that $f^{-1}(f(A))=A$

I am taking a basic course on proof and trying some questions on relations and functions I am trying from the very basic please understand my poor proving skills :( I believe I have to use the definition of the image and the inverse image of f to…
slowpoke
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Prove that there are no positive integer solutions. Please check my proof.

Edit: Thank you for the help. It makes much more sense now. I'm trying to learn proofs on my own, and I would really appreciate any feedback for my proof below. Are there any logical errors? Is there a better way to do this? thanks very much in…
Mari
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Prove that $E$ closure is closed

Always thank you for helping me out I was following my professor's proof and this is how it goes Prove that $E$ closure is closed let $x$ be a limit point of $\operatorname{cl}(E)$, claim: $x$ is in $\operatorname{cl}(E)$ By the definition of a…
slowpoke
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For every real number, a, there's another real number, b, when squared equals a

I'm tasked with figuring out if the following statement is correct. $$ \forall r \in \mathbb{R}, \exists s \in \mathbb{R},s^2 =r $$ Right now my understanding is that the set of real numbers includes negative numbers. Assume r is a negative real…
Abir Taheer
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If $n =\log\left(\frac{\mu}{1-\mu}\right)$, how to show $-\log(1-\mu)=\log(1-e^n)$

Given $$n =\log\left(\frac{\mu}{1-\mu}\right)$$I need to show that$$ -\log(1-\mu)=\log(1-e^n) $$ From the first equation, $$ -\log(1-\mu)=-\frac{n}{\log(\mu)} $$ If the question is valid, it means that I can…
wd violet
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Let $N \in \mathbb{R}$ such that $N \geq 3$ and $q > 1$. Show that $\frac{1}{2^*} - \frac{2}{N(q-1) - 1} < 0 \iff q < 2^*$.

Let $N \in \mathbb{R}$ such that $N \geq 3$, $q > 1$ and $2^* := \frac{2N}{N - 2}$. Show that $\frac{1}{2^*} - \frac{2}{N(q-1) - 1} < 0 \iff q < 2^*$. I would like to know how to prove the statement above. I tried to prove it, but I…
George
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How can I prove that $c^n$ is upper bound of $n^k$?

The proof can be using calculus or finding a $n_o$ from which it holds that $c^n>n^k$ for $k \ge 1$ and $c>1$
Cate
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