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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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Prove that $a_1^2+a_2^2+\dots+a_n^2\ge\frac14\left(1+\frac12+\dots+\frac1n\right)$

Let $a_1,a_2,\dots,a_n$ be non-negative real numbers such that for any $k\in\mathbb{N},k\le n$ $$a_1+a_2+\dots+a_k\ge\sqrt k$$ Prove that $$a_1^2+a_2^2+\dots+a_n^2\ge\frac14\left(1+\frac12+\dots+\frac1n\right)$$ I just want to verify my…
user164524
2
votes
1 answer

Proving that lines from any vertex of a parallelogram to the midpoints of the opposite sides trisect a diagonal

I'm asked to prove algebraically that the lines from a vertex of a parallelogram to the midpoints of the opposite sides trisect a diagonal. I did something like this Then I got the slopes of the three lines (the two lines from the vertex and the…
user87870
2
votes
1 answer

Is my proof valid? Integration of logarithmic function.

After this question: $$\int\ln(1+ae^{bx})\\=\int\left(ae^{bx}-\frac{a^2e^{2bx}}2+\frac{a^3e^{3bx}}3+...\right)\\=-\frac1b\left(\frac{-ae^{bx}}1+\frac{a^2e^{2bx}}{4}-\frac{a^3e^{3bx}}{9}...\right)\\=-\frac1b{\rm Li}_2(-ae^{bx})$$ If this is wrong,…
RE60K
  • 17,716
2
votes
1 answer

Proof Verification (Set Theory)

Let $S$ be a set with $N$ elements and let $A_1,\dots ,A_{101}$ be $101$ (possibly non disjoint) subsets of $S$ with the following properties: a) each element of $S$ belongs to at least one of these subsets b) each subset contains exactly $1000$…
user211111
  • 21
2
votes
3 answers

Is this a valid way to prove that $\frac{d}{dx}e^x=e^x$?

$$e^x= 1+x/1!+x^2/2!+x^3/3!+x^4/4!\cdots$$ $$\frac{d}{dx}e^x= \frac{d}{dx}1+\frac{d}{dx}x+\frac{d}{dx}x^2/2!+\frac{d}{dx}x^3/3!+\frac{d}{dx}x^4/4!+\cdots$$ $$\frac{d}{dx}e^x=0+1+2x/2!+3x^2/3!+4x^3/4!\cdots$$ $$\frac{d}{dx}e^x=…
Teoc
  • 8,700
2
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2 answers

How to identify an error in a proof?

Right now I'm studying how to find errors in proofs by looking for common mistakes such as circular reasoning, using examples etc. I haven't had too many problems for the most part but I've run into a proof for which I can find no errors. It goes as…
Johnathan Scott
  • 333
2
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1 answer

Trivial mathematical analysis problem

Let $\mathbb{R} \supset E \neq \varnothing$. Put $\alpha = \sup E $. Then, for all $n \in \mathbb{N}$, $\alpha - \frac{1}{n} $ is not an upper bound of $E$, but $\alpha + \frac{1}{n}$ is an upper bound. Solution We have $\frac{1}{n} > 0 $ for all…
user195835
2
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3 answers

Proof that $A\cap B$ and $A-B$ are disjoint

119. Prove or disprove that $A\cap B$ and $A-B$ are disjoint: Consider that $A\cap B=\{x|x\cap A\text{ and }x\cap B\}$ and that $A-B=\{x\in A|x\notin B\} $ So, to translate this question: “Prove or disprove that the set of elements that exist in…
123
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1 answer

How do I go about solving these two proofs?

Show that the follow statement is true: If $ x \in \mathbb{R}$ such that $x^2+1=0$ then $x^4=\pi$ Constructive proof: If $x,y$ $\in \mathbb{R}$ such that $x \lt y$, show that $\exists \ z\in\mathbb{R}$ such that $x\lt z\lt y$
janny
  • 305
1
vote
1 answer

Proving that $(A^t)^t=A$

$(A^t)^t=A$ $(A^t)^t-A=0$ $(A^t)^t-A=A-A\rightarrow (A^t)^t=A$ Is this proof is valid or do I need to add more information to make it more clear?
gbox
  • 12,867
1
vote
3 answers

Prove that $\sqrt[4]{1+y^4} \leq 1+|y|$

Prove that $\sqrt[4]{1+y^4} \leq 1+|y|$ for all real values of $y$. I attempted to show this by finding the power series expansion of $\sqrt[4]{1+y^4} $ and then relating that to $1+|y|$; however, I have made little progress. Any advise?
tachyon_man
  • 23
1
vote
2 answers

Proof irrationality $n\sqrt{11}$

Prove that $\sqrt{11}$ is irrational, subsequently prove that $n\sqrt{11}$ is also irrational for every $n \in \mathbb{N}$. You are allowed to use that if $p$ is prime, and $p | a^2$, then $p|a$. Can't you also prove that $n\sqrt{11}$ is…
Dolma
  • 67
1
vote
1 answer

Prove that the maximum number of diagonals that can be drawn in convex n-sided polygon

My attempt: Let the maximum number of diagonals of such an n-sided convex polygon = D(n) For example a triangle has 0 diagonals therefore D(3)=0, similarly a quadrilateral by definition can only have 1 diagonal so D(4)=1. Assume that…
PatrickSwarthmore
  • 13
1
vote
2 answers

Prove or disprove - If a divides b and b divides a does a=b

Prove or disprove: If a, b belong to the set of positive integers, and if a divides b and b divides a, then a=b. Does this hold if if a,b are not necessarily positive? Why or Why not? Here is what I have: If a and b are integers, we say a divides b…
123
  • 1,708
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0 answers

Has the abc conjuncture been proved by Shinichi Mochizuki?

I'd like to know is his proof was reviewed, and what exactly happened.
user3758041
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