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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.

21426 questions
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Is the inscribed angle theorem always true?

The inscribed angle theorem states that $\angle O=2\times\angle B$. The theorem is true for when point $B$ is located between points $A$ and $C$ relative to the perimeter. But what would happen if $B$ was located exactly at $A$ or $C$? Angle $B$…
ShootinLemons
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Is the sequence increasing or decreasing?

I have the sequence $a_n = \frac{3^n}{1+3^{2n}}$ and I'm trying to find if it's increasing or decreasing. I used the formula $\frac{a_n}{a_{n+1}}$ to get $\frac{a_n}{a_{n+1}}=\frac{1+3^{2n+2}}{3(1+3^{2n})}\geq 1$. Therefore, the sequence is…
jlb0720us
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To verify if this is a valid move?

I am playing around with some numbers and it looks like this: $$\begin{align}e^{-3ix}&=\cos3x-i\sin3x=(\cos x-i\sin x)^3\\4\cos^3x-3\cos x-i(3\sin x-4\sin^3x)&=4(\cos^3x+i\sin^3x)-3e^{ix}\end{align}$$ Expanding $e^{-3ix}=(\cos x-i\sin…
xxxx036
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Intersection of sets of rational numbers

I have sets $A = \{1/n \mid n \in \mathbb{N}\}$ and $B = \left\{\frac{k}{2^n} \mid k,n \in \mathbb{N} \right\}$. Am I correct that $A \cap B$ is exactly $\frac{1}{2^n}$? Certainly I need to have numerator $1$, but I'm worried that there could be…
Brad G.
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Positive integers partitioned using arithmetic progression

The set of all positive integers is partitioned into several(finitely many) arithmetic progressions. Show that there is at least one among these arithmetic progressions whose initial term is divisible by its difference. my attempt is as follows…
m3h3mm3d
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Positive Definite implies invertible Matrix: Is this enough to prove it?

If $A$ is PD, then $A$ is invertible. Proof: Let $x\in\mathbb{R}^{n}$ such that $x\neq0$. If it weren't the case that $A$ is invertible, then: $$ Ax=0\implies x^{T}Ax=0 $$ not positive definite. Hence, proof complete. My question is, if this is…
ZeinabQom
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Proof by Contradiction Involving Inequalities

I am attempting to prove a result (does not have to do with inequalities) using proof by contradiction. We know that by assuming the proposition P and for some quantity $x$ related to P, $4 \le x \le 10$. However, if I assume not P, I arrive at…
mosalah111
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Inequality proof using Induction. Prove or Disprove.

I need to prove or disprove this inequality. So I am not too sure if the inequality even holds, Intuitively it does. Prove or Disprove: $\dfrac{1}{n} < \dfrac{n-1}{n^2 - 2n}$ for any natural number > $3$. My Work: Base Case: $n=4$ $\dfrac{1}{4} <…
hydra-bslash-0
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Proof that if $A$ is a subset of $B$ and $C$ is a subset of $D$, then $A \setminus D$ is a subset of $B \setminus C$.

Started my proof by assuming that $A \subset B$ and $C \subset D$. Then I proceeded by supposing that $x \in A \setminus D$. So $x \in A$ and $x \notin D$. Is it valid to conclude that $x \notin C$ since $C \subset D$? I'm assuming it is always…
user917023
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Is my proof using squeeze theorem correct?

I have to prove using squeeze theorem that limit of $(1.3.5...(2n-1))/(2.4.6...2n)$ tends to 0 as n tends to infinity. My attempt: $1/(2.4.6...2n)\leq u_n\leq ((1.3.5...(2n-1))/(2.2.2...2n)$, where $u_n$ is the given sequence. Thus we…
Natasha J
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Prove there is no integer solution to $a^2 - b^2 = 2$ by contradiction

I have been trying this question for a long time, as a similar one will be in my test next week. I have done this: $a^2 - b^2 = 2 $ $a^2 = 2 + b^2 $ $a = \sqrt2 + b$ As $\sqrt2$ is not an integer, and if b is an integer, adding them together will…
Guillermo Aguilar
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Is this a valid proof that absolute value of $\ln(1-x) > \ln(1+x)$ for $0 < x< 1$?

I used CodeCogs to create the equations in the proof. Is there any way to directly use asciimath or something else?
Ken Smith
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Is this proof about sequence correct?

I have to prove that $u_n=4^{3n}/3^{4n}$ is a null sequence. My attempt: $1/3^{4n}<4^{3n}/3^{4n}<1/3^{n/4}$ Taking limits and by squeeze principle the limit $u_n=4^{3n}/3^{4n}$ tends to 0. Is this correct?
Natasha J
  • 825
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Show that if $f(x)>g(x)$ then $\exists e > 0 : f(x) > g(x) + e$

Let $f,g:[a,b] \to \mathbb{R}$ be two continuous functions, with $f(x)>g(x), \forall x \in [a,b]$. Show that $\exists e > 0, $such that $f(x)>g(x)+e$. My try is:Let $h(x) = f(x)-g(x), h:[a,b] \to \mathbb{R}$. Then $h$ is continuous in $[a,b]$, and…
average_discrete_math_enjoyer
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Erroneous proof involving cartesian products?

The problem is: prove if A, B, and C are sets and $A \times C = B \times C$, then A = B. I decided to prove it and wrote this proof: Proof. First we will show that if A, B, and C are sets and $A \times C = B \times C$, then $A \subseteq B$. Assume…
mont2223
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