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Questions tagged [proof-verification]

For questions concerning a specific proof or a specific solution, asking for verification, identifying errors, suggestions for improvement, etc. (You should not use this tag if the question does not contain a proposed proof/solution.)

For questions concerning a specific proof (or a proof sketch) or a solution to some problem; asking a question with this tag indicates one would like answers to respond broadly as to the following:

  • Verification of the proof/solution;
  • Identifying errors in the proof/solution;
  • Suggestions for improving the proof/solution;
  • Alternative approaches.

Also, consider the related tags and .

22798 questions
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helmholtz decomposition - Can't follow steps

I'm trying to follow the proof for the derivation of helmholtz decomposition from wikipedia, however, I can't figure out how the negative sign changes into a positive. If some one can help that would be great. The attached picture shows where I'm…
Mr Smokey
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$\binom{n}{k} \in N$

We observe from Pascal's triangle that $$\binom{n+1}{k}=\binom{n}{k-1}+\binom{n}{k}$$ We prove this statement correct by expanding the right side: $$\frac{n!}{(k-1)!(n-k+1)!}+\frac{n!}{(k)!(n-k)!}\rightarrow\frac{(n+1)!}{k!(n-k+1)!} $$ Next we…
Misha.P
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Can this method be used to prove a number is transcendental?

Suppose we want to prove that some number $x$ is transcendental. Can we do so by proving that $$x^n\ne\frac{a}{b}$$ where $a, b, n \in \Bbb{Z}$ where $n \ne 0$? The reasoning behind the statement is as follows: Consider a polynomial equation: $0 =…
Badr B
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Why does $\frac {100 - 100}{100 - 100}$ give 3 answers?

I recently saw a Maths Problem, to which I got 3 different answers, all of which seem correct. Case 1 $\frac {100 - 100}{100 - 100} = \frac{0}{0} = \infty$ Case 2 $\frac{100-100}{100-100} = \frac{(100-100)\div(100-100)}{(100-100)\div(100-100)} =…
Mrigank Pawagi
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Proof verification: If $n \in \mathbb{N}$, then $C(2n, n)$ is even

Working on improving my proof-writing abilities, so working through Hammack's Book of Proof. One of the exercises is as follows: If $n \in \mathbb{N}$, then $C(2n, n)$ is even. My proof differs from the one given, and I am hoping someone can…
pinniped
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Is the following a valid proof of the $\frac{0}{0}$ case of L'Hôpital's rule?

Let $\displaystyle \lim_{x\to c}~f(x)=\lim_{x\to c}~g(x)=0$ and $g'(c)\neq0$, Edit: Assume also that $c$ lies in the open interval $S$, and that $f(x)$ and $g(x)$ is continuous on $S$, Then consider $\displaystyle \lim_{x\to c}\frac{f(x)}{g(x)}$,…
joshuaheckroodt
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Induction and Cardinality questions.

I just had my exam today and I encountered some interesting problems that I need some help clarifying. Question 1: If $n \in \mathbb{Z}$ Prove that $n^3<3^n$ for all of $n\ge 4$. The method that I used to solve the above is induction: Basis: Let $n…
Sam Kay
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How to prove expression correct

Prove that for any positive integer $n $: $(2n)!$ is divisible by $({n!}) ^2: $ If you know a solution to the problem, please help.. Sorry, this problem was edited by another user who changed some values. I have now fixed the problem.
Jmaxmanblue
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Square area equal to difference between the circumscribed circle and the inscribed circle

There is no such square whose area is equal to the difference between the areas of its circumscribed and inscribed circles. Am I right? Imagine a square with length $L$. This square has an area of $L^2$. Its inscribed circle has radius…
For the love of maths
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Multiplying Absolute Values

How do I multiply a non-absolute value with an absolute value? For example: |x-1| to be multiplied with x^2? I got an answer of x^2|x-1| but I'm pretty sure it's wrong. Thank you!
shhh
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Proof: For a real matrix $A$, $A=A^T$ if and only if $A=Q\Lambda Q^T$, where $QQ^T=I$.

WLOG, we assume that $\mathbf{A}$ is an $n$ by $n$ real and symmetric matrix, $\lambda_1, \ldots, \lambda_n$ are eigenvalues, and $\mathbf{s}_1, \ldots, \mathbf{s}_n$ are eigenvectors of size $n$ by $1$, corresponding to $\lambda_1, \ldots,…
Danny_Kim
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is my proof wrong?

I have to find two functions such that one is surjective and the composition of them is not,so I chose $I:\Bbb N \mapsto \Bbb N$, $I(x)=x$ and $j:\Bbb R \mapsto \Bbb R$, $j(x)=x$ Both are surjective and the composition of them is $l(j(x))$…
john
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Verify already written proof

I wrote a proof and I'm really just here to make sure my argument is making sense. For all x>=0, (x^2)-x is even. Base case: x=0. (0^2)-0 is even. Inductive Step: x>= 0. Suppose (x^2)-x is even. Then there is an integer y so that (x^2)-x = 2y …
user503376
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