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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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Proof that for any real number $x$, $-|x| \leq x \leq |x|$. Is my proof too good to be true?

This comes from one of the exercises in How to Prove It by Daniel Velleman. In this proof I invoke the theorem from the previous exercise: “for all real numbers $a$ and $b$, $|a| \leq b$ iff $-b \leq a \leq b$.” I won’t include that proof here, as I…
i-cant-name
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How do I check if a list of numbers have the same remainders when divided by the same number

I am watching a video which explains that "when you divide by the number n, there are n possible remainders: 0, 1, 2 .... , n-1". Then, the author says that when you are given a list of numbers starting from: 9, 99, 999 and 999......999 (2010 9s),…
ilovetolearn
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Proof by contradiction that an expression is irrational

The question is: Proove that $\left(\sqrt[3] \frac{q^2-1}{qx}\right)$ is irrational if x is irrational and nonzero and q is a rational number that is not 0 or 1. I started my proof with: To get a contradiction, suppose that $\left(\sqrt[3]…
Name
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Lecture notes proof verification - Intermediate Value Theorem

In the model proof below for the Intermediate Value Theorem it is written that $L_p=\{y\in[a,b]\quad\text{such that}\quad f(y)\lt{q}\}$. Then $c\in{L_q}$ but $d\notin{L_q}$. Shouldn't it be that $a\in{L_q}$ but $b\notin{L_q}$ because…
user503154
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Proof verification for bounded sets.

Is my proof for set boundedness correct? Proposition: Let $A\subseteq \mathbb{R}.$ Then $A$ is bounded if and only if $\exists{K}\gt{0}$ s.t $\forall{a}\in{A}, |a|\leq{K}$. Proof: Suppose that $A$ is bounded. Then there exists $M\in \mathbb{R}$ and…
user503154
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Proof: $n^2 - 7$ is not divisble by 5

I tried to prove that $n^2 - 7$ is not divisible by $5$ via proof by contradiction. Does this look right? Suppose $n^2 - 7$ is divisible by $5$. Then: $n^2 - 7 = 5g$, $g \in \mathbb{Z}$. $n^2 = 5g + 7$. Consider the case where $n$ is even. $(2x)^2…
Omaroo Baniessa
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Given $a \in \mathbb Q$ which is non-zero, show that $1/a \in \mathbb Q$.

Any idea? I've started with $a= p/q$, meaning $q$ has to be rational. Then $1/a= q/p$ But surely this could be irrational if, say $p=9$, $q=4$?
AnoUser1
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How is this simplified? $\frac{n(2n^2+9n+1)}{6}+(n+1)^2+2(n+1)-1$

How do we simplify this: $$\frac{n(2n^2+9n+1)}{6}+(n+1)^2+2(n+1)-1$$ to this: $$\frac{(n+1)(2(n+1)^2+9(n+1)+1)}{6}$$ What were the steps taken to get to it?
Amir Šaran
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proof of uniqueness regarding division with remainder

Let $m,n \in N$ with n>0, then there exists $q,r \in N$ such that $m=qn+r$ with $0\le r < n$ Show for any given $m,n$ with $n>0$ the $q$ and $r$ are unique. So if $m=q_1n+r_1=q_2n+r_2$ with $0\le r_1\lt n$ and $0\le r_2< n$ then $q_1=q_2$ and…
Carlos Bacca
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Prove that $\sqrt{2} + \sqrt{17}$ is irrational. Is my proof correct?

$2+17 = a^2/b^2$ $19b^2 = a^2$ ($a$ is divisible by 19) $19b^2 = (19k)^2$ $19b^2 = 361k^2$ $b^2 = 19k$ ($b$ is divisible by 19) Since both numbers are divisible by 19,it means they have a common factor. Is this accurate? If not,please…
user569685
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Prove For each integer $n \ge 1$ $\sum_{i=1}^{n} i^2=\frac{n(n+1)(2n+1)}{6}$

Did I do this correctly? (basis) $\sum_{i=1}^{1} i^2=\frac{1(1+1)(2(1)+1)}{6}$ thus both sides are equal to 1. (induction) Fixed $n$ and $k$ to be natural numbers. Assume $n=k$, then $\sum_{i=1}^{k+1}i^2= \frac{k(k+1)(2k+1)}{6} + (k+1)^2$ by…
George
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Proof of potential equation

I want to proof that:$\frac{exp(8)}{exp(8)+exp(10)}=\frac{exp(0)}{exp(0)+exp(2)}$ So, my idea is to inverse the fraction and split it. I'd end up with $1+exp(2)$ which is the inverse of the right side of the equation. Is inversing necessary or even…
Max
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How to prove $f:Z \to E$, given by $f(x) = 2x$ is bijective?

I know I must prove that $f$ is both injective and surjective. I've got the injective proof down. But I'm stuck on the surjective proof. So far I have, for some $x,y ∈ Z$, $y = 2x \Rightarrow x = y/2$. Now does this prove that $f$ is surjective as…
johntc121
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How do we proof this in integers modulo n.

Let's say we have four integers, $\phi$, $\theta$, $\omega$ and $\zeta$. Where we define $\omega$ and $\zeta$ to be co-prime. What I have to show (or prove?) is the following statement: The equivalence classes of R match with the elements of the…
Cro-Magnon
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Proving continuity of Logarithm using $\delta$-$\epsilon$

Say we wanted to prove the continuity of the logarithm using the $\delta - \epsilon$ proof (and using the definition of the log as the inverse of the exponential). For any log base $a>1$ Starting with $|\log_a({x_1}) - \log_a({x_2})|<\epsilon$, We…
Riley H
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