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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Lagrange identity

I'm trying to prove the Lagrange identity. There seem to be multiple results with this name, some with slight variations, but the exact identity I have in mind is $$ \left(\sum\limits_{i=1}^n a_i b_i \right)^2 = \left(\sum\limits_{i=1}^n…
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Is my proof of showing "$r^2+2rs+s^2$ is composite for all positive integer $r$ and $s$" correct?

Hi again a question on if my proof is correct, since the way it is written differs much with how the book proofs it.. The Question given is : "$r^2+2rs+s^2$ is composite for all positive integer $r$ and $s$" Here's the proof I have written : Assume…
Diceble
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Critique my proof of $\lvert x \rvert + \lvert y \rvert \leq \lvert x + y \rvert + \lvert x - y \rvert, \ x,y \in \mathbb{R}$

Critique my proof of $\lvert x \rvert + \lvert y \rvert \leq \lvert x + y \rvert + \lvert x - y \rvert, \ x,y \in \mathbb{R}$ Let $x, y \in \mathbb{R}$. Case #1: $x = y$ $\Rightarrow \lvert x \rvert = \lvert y \rvert$. Hence, $$\lvert x + y \rvert =…
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Is this function surjective

I have a function $f :\mathbb R \times\mathbb R\to\mathbb R$ defined by $f(x,y)=x+y$ and I am struggling to determine if it is surjective or not. I already showed it is not injective. I know that if it is surjective I need to find some $z$ inside…
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Proof for: if there exists an injection $\mathbb{N}_m \rightarrow \mathbb{N}_n$, then $m \leq n$.

Definition of $\mathbb{N}_m$ is a set $\{x \in \mathbb{Z}^+ | 1 \leq x \leq m\}$. The book "An introduction mathematical reasoning" by Eccles has this proof written out on 3 pages. They use induction on $n$ to prove it. But I fail to see why you…
Naz
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Can an even function ever be injective?

In the first few lessons of an introductory Calculus class, there is this exercise: We say that a function $f$: $R → R$ is even if $f(−x) = f(x)$. Can an even function ever be injective? My proof is as follows and I am wondering if it is…
Claire
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$\textstyle\displaystyle{\sum_{a_1,\dots, a_n\geq 1}\frac{1}{\prod_{i=1}^{n}a_i\sum_{i=1}^{n}a_i}}=n!\zeta(n+1)$

$\underline{\text{Motivation}:-}$ Recently I saw this video from Micheal Penn. After seeing the entire video I realized that all the things he did can be easily generalized. In that video he showed, $\textstyle\displaystyle{\sum_{m,n\ge…
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Is this proof about limit of a sequence correct?

I have to prove that if $f_n$ is convergent and $g_n$ is divergent to positive infinity then show that $lim\frac{f_n}{g_n}$=$0$. My attempt: Since $f_n$ is convergent, it is bounded. This implies, $|f_n|\leq G\epsilon$. And since $g_n$ is divergent,…
Natasha J
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Is this proof about sequences correct?

Let $(u_n)$ and $(v_n)$ be two real sequences with limits L and M respectively. If $x_n$= max$({u_n,v_n})$ and $y_n$=min$(u_n,v_n)$, prove that the sequence $x_n$ and $y_n$ converges to max$(L,M)$ and min$(L,M)$ respectively. My attempt: It is given…
Natasha J
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Proving the distributive lattice $D(n)$ is boolean

Let $n$ be a positive integer and let $D(n)$ be the set of positive divisors of $n$. Prove that the distributive lattice $(D(n); |)$ is boolean iff $n$ is square-free. Let $(D(n),\wedge,\vee,')$ be boolean where the operators are defined…
Manjoy Das
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Proof verification: sequence $ a_n = (-1)^n $ does not converge

Theorem: Show that the sequence $ a_n = (-1)^n $ for all $ n \in \mathbb{N}, $ does not converge. Proof: Suppose that there exists a limit $L$ such that $ a_n \rightarrow L $. Specifically, for $ \epsilon = 1 $ there exists $ n_0 $ s.t. for all $ n…
hazelnut_116
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Equation with $ \sqrt[5]{}$

How to show that this equation $ \sqrt[5]{20-2x} + \sqrt[5]{7-x}+\sqrt[5]{3x+5}=2$ have 3 solutions 9, -6 and -25 Wolframsays the equation have no solutions !
Pascal
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Beta and Gamma functions relation proof.

I found a proof of the Beta-Gamma functions relation, but I don't understand what happened between 3rd and 2nd last line. There was s^z and in the next line there is s^(z-1). Where did it come from? Or is the proof incorrect? Can anyone explain it,…
Sway
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Is my reasoning sound for proving that the intersection over a family of sets is empty?

So as a homework problem I was asked to find the intersection of the following family of sets. I was told that my reasoning was invalid as I did not correctly prove that the intersection is the empty set. Is the fact that $\displaystyle \frac{1}{n}…
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A non-combinatorial inductive proof

It is given that each person in the group of n persons has at least half of the persons in the group as his friends.It is required to prove that it is possible to seat them in a circle so that everyone sits next to a friend of his or hers.Here,I…
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