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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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Every symmetric bilinear form has a orthogonal basis

Task: Assume $K$ is a field, $V$ is a vetor space over $K$ and $\langle -, - \rangle$ a symmetric bilinear form on $V$. Show that $V$ has a orthogonal basis. Solution: Define $A := \{v \in V | \langle v, u \rangle = 0 \forall u \in V\}$, and let…
Julian
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Proof $a + b \le c $ implies $\log(a) + \log(b) \le 2\log(c) - 2$

I have to proof the following statement: Assume $a, b$ and $c$ are natural numbers that are different of $0$. If $a + b \le c $, then $\log(a) + \log(b) \le 2\log(c) - 2$. All $\log$ functions are the second $\log$ functions, thus…
Pieter Verschaffelt
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Eight points are in/on the circle of radius 1cm. Show that distance between some two points is less than 1cm.

Original problem If 8 points in a plane are chosen to lie on or inside a circle of diameter 2cm then show that the distance between some two points will be less than 1cm. My proof Let the points be $p_1,p_2,\dots,p_8$ Placing point $p_8$ at the…
Singh
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$\varepsilon-\delta$ proof of $\lim_{x \to -\infty} \frac{1}{1+x}=0$

I do not have a clue about where to start. If I'm right, I need to find a relation between $\varepsilon$ and $\delta$ such that $0<|x + \infty|<\delta$ implies $|\frac{1}{1+x}|<\varepsilon$. Is this wrong? What else should I do?
Maurice J
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Find the number of days in which the job would be finished

$P_1$(person) can complete a job in $1^2$ day, $P_2$ can complete the same job in $2^2$ days. In general $P_n$ can complete the job in $n^2$ days. In how many days the job would be finished if an infinite number of distinct people do the job…
AhmedBajwa
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How is this not a proof of the proposition "$\text{If}\;a > 0 \;\text{then}\; (b > 0 \Leftrightarrow ab > 0) $"?

The question I got on my exam was $$\text{If}\;a > 0 \;\text{then}\; (b > 0 \Leftrightarrow ab > 0) $$ The answer I put was "recall the mutiplication rule from the inequality axioms of real numbers". I will put it for reference. $$a < b …
Recker12
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If $0 < x < y$, then $x^n < y^n$

The problem asks to prove that if $0 < x < y$ then $x^{n} < y^{n}$, where $n$ is a positive integer, so I started by assuming that $0 < x < y$. I then wrote this chain of inequalities: $x^{n} < x^{n-1}y^{1} < x^{n-2}y^{2} < x^{n-3}y^{3} < ... <…
Joao Konno
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gcd(2a+1, 9a+4) = 1

The question is from Burton's Elementary Number Theory. I want to know if my proof is legible. Proof : Let $$d=gcd(2a+1, 9a+4)$$ Then $$d|2a+1$$ and $$d|9a+4$$ $$2a+1=db$$ and $$9a+4=dc$$ $$ a = \frac{db-1}{2}$$and$$a= \frac{dc-4}{9}$$ Equating…
P.Jo
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Denote $f(x)=\int_x^{x+1}\cos t^2 {\rm d}t.$Prove $\lim\limits_{x \to +\infty}f(x)=0.$

Problem Denote $$f(x)=\int_x^{x+1}\cos t^2 {\rm d}t.$$Prove $\lim\limits_{x \to +\infty}f(x)=0.$ Proof Assume $x>0$. Making a substitution $t=\sqrt{u}$，we have ${\rm d}t=\dfrac{1}{2\sqrt{u}}{\rm d}u.$ Therefore, \begin{align*} f(x)&=\int_x^{x+1}\cos…
mengdie1982
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Is this proof for $\sum^n_{i=1} i= \frac{n^2+n}{2}$ correct?

Is this proof correct, as I feel unsure about whether or not I did that correct because the book did it differently, I wouldn't know however why my proof should be wrong. Could you help me out? The following statement is to be proven by…
thebilly
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Induction verification: Prove that $2^n < n!$, for all natural numbers $n > 3$

Prove that $2^n < n!$, for all natural numbers $n > 3$ My proof: Basis step: When $n = 4$, $2^4 = 16 < 4!=24$ which is true. Inductive step: Assume that $2^k < k!$ for any $k > 3$. We must show that $2^{k+1} < (k+1)!$. Since $(k+1)! = (k+1)\cdot…
user502227
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Please check my proof for $\sup AB=\sup A \sup B.$

Problem Assume $A \subset \{x|x \geq 0, x \in \mathbb{R}\}$ and $B \subset \{y|y \geq 0, y \in \mathbb{R}\}$. $A,B$ are both nonempty and bounded. Define $AB=\{xy|x \in A,y \in B\}.$ Prove $\sup AB=\sup A \sup B.$ Proof If $\sup A\sup B=0$, then…
mengdie1982
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Is this proof for if $0 < a < b$ then $a^2 < b^2$ correct?

I'm reading the book 'How to prove it' from Daniel Velleman which he presents a proof for the following; if $0 < a < b$ then $a^2 < b^2$ as; Proof. Suppose $0 < a < b$. Multiplying the inequality $a < b$ by the positive number $a$ we can conclude…
redbandit
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Proving the inverse of $r_h$ is $r_h$

How would you prove the following proposition... The inverse of $r_h$ is $r_h$ where $r_h$ is a horizontal reflection and we are in the Euclidean plane. I was thinking something like this, but I don't think I have it quite right... If $r_h$ is the…
user6259845
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Starting with a string AB. Is it possible to obtain BA following these rules?

Starting with a string AB. One is allowed to add, or remove any occurrence of AAA, BB, or ABAB anywhere in the string . Is it possible to obtain BA? My attempt at proof of impossibility below: In the proof, I will write about "creating a string X…
Adam
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