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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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For each $n \in \mathbb{N}$, define $S_n = \{m \in \mathbb{Z}:m \leq n\}$. Prove that $\bigcup\limits_{n\in \mathbb{N}} S_n = \mathbb{Z}$

For each $n \in \mathbb{N}$, define $S_n = \{m \in \mathbb{Z}:m \leq n\}$. Prove that $\bigcup\limits_{n\in \mathbb{N}} S_n = \mathbb{Z}$ So far I have: Let $x \in \mathbb{Z}$. Assume by contradiction that $x \notin \bigcup\limits_{n\in \mathbb{N}}…
Owen Murray
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Real analysis solution

Let $f:\mathbb{R}\to\mathbb{R}$ be a differentiable function such that its derivative $f'$ is a continuous function. Moreover, assume that for all $x\in\mathbb{R}$,$$0\leqslant \vert f'(x)\vert\leqslant \frac{1}{2}$$Define a sequence of real…
zaemon_23
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Is manipulating an unproven statement into a true one a valid way to prove it?

Let's say we need to prove $$\frac{1}{2} = \frac{2}{4}$$ (as an example) Usually, $\frac{1}{2}$ is manipulated into $\frac{1 \cdot 2}{2 \cdot 2}$, which is $\frac{2}{4}$. So we ended up with what we're trying to prove. Is it possible to prove this…
UserX2021
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Prove: if $a \cdot x = b \cdot y$ for all $x,y \in \mathbb{Z}$ then $a = b = 0$

I'm starting to do mathematical proofs by myself, and I have found this: $\quad\forall x,y \in \mathbb{Z}\quad$ if $\quad a \cdot x = b \cdot y \quad$ then $\quad a = b = 0$ Proof: Lets prove it by contradiction: If $\quad a\neq b \Rightarrow a…
DaguCode
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Is this irrationality proof valid?

We aim to prove that $\sqrt{6}$ is irrational. Consider the polynomial $p(x) = x^2 - 6$ Note that $p(\sqrt{6}) = (\sqrt{6})^2 - 6 = 0, $ hence $\sqrt{6}$ is a root of $p(x)$. Now, consider the Rational Root Theorem, which states that any rational…
mykull
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SOLUTION VERIFICATION - demonstrate that the bigger the number is the more cubes are between an interval...

Can we demonstrate this fact: that the bigger the numbers are the more cubes are between $10^n$ and $2*10^n$? I need this to solve a problem. Here is my idea. I think we have to show that if $10^x≤a^3≤2∗10^x$, $10^y≤b^3≤2∗10^y$ and $x
IONELA BUCIU
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How do I prove that for every positive real number $a$, the equation $e^{-x} = ax$ has a real solution $x>0$?

How do I prove that for every positive real number $a$, the equation $^{-}=a$ has a real solution $x>0$? What I tried: I tried moving everything to one side leaving the other side as $0$. Then I drew up a graph of the $e^{-x}$ and the $ax$ line…
thetrueembodimentofstupidity
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Proof that $ \frac{5}{n+1}$ converges to $0$ as $n$ approaches infinity

I recently began real analysis and I just wanted to make sure my proofs make sense. I know how you prove $ \frac{1}{n}$ but not sure how the constant in the sequence changing from 1 to 5 affects the proof. Below is my take on this: Prove $…
Bill Cogn
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Is there an established conjecture for prime triplets of the form (p - 2, p, p + 2)?

Conjecture: There exists no prime number p > 5 such that both p + 2 and p - 2 are prime numbers. Formal Proof: Consider any prime number p greater than 5. p is an odd prime number, and therefore: p - 2 and p + 2 are both odd numbers. Every set of…
Martin.s
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Prove that if $xy>0$, then either $x>0\ \&\ y>0$ or $x<0\ \&\ y<0$

Theorem: $$x\cdot y>0 \implies (x>0 \ and\ y>0)\ or\ (x<0\ and\ y<0)$$ Proof: Suppose $x\cdot y>0$. If either $x$ or $y$ are $0$, then $x\cdot y=0$ which is a contradiction, so both $x$ and $y$ must be $\ne0$. This leaves four remaining…
Vulgar Mechanick
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Strictly monotone $f$ implies $f$ has at most one root

After I reas the section about the Rolle's lemma and Mean Value Theorem, there were examples about a function that has exactly one root in a certain closed interval. The existence of a root was clear to me, and the uniquenesswas justified by Rolle's…
Mr.MathDoctor
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Proof that a relation $S$ is an equivalence relation

Let $X$ be an uncountable set. On the set $P(X)$ (this is the power set) we define a relation $S$ by saying that $(A,B) \in S$ iff $A\backslash B$ (equivalent with this notation: $A-B$) is a countable set. Oh, woops, I forgot to mention that $A \in…
user34
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Uniqueness-proof

I am currently trying to solve example 3.7.2 from Velleman's how to prove it. Here is the problem: Prove that there is a unique positive real number m that has the following two properties: (a) For every positive real number $x$, $x/(x+1)
eeqesri
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Given pedersen commitments of some elements, how to prove that the sum of only one subset of these elements is equal to the given element θ？

Assume that Prover have $n$ pedersen commitments ($V_{a_1},V_{a_2},\cdots,V_{a_n}$ where $V_{a_i}=G \cdot a_i + H \cdot r_{a_i}$) of $n$ elements $a_1,a_2,\cdots,a_n$. The Prover have another element $\theta$. The verifier is provided with these $n$…
user105684
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How to find the recurrence relation of an increasing-decreasing sequence?

The question is: If we have a sequence of $n$ numbers from $1$ to $n$, and we have: $a_1 < a_2$ and $a_2 > a_3$ and $a3 < a4$ and so on, alternating between increasing and decreasing, what is the recurrence relation describing the number of such…
ArminAshrafi
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