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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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Can an open ball be closed if the open ball contains infinite points?

Consider a metric space $(X,d)$. Is the following statement true? An non-finite open ball in X with finite radius is never closed. Non-finite in this sense means that the open ball contains an infinite amount of points.
Birdman
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Use semantics to prove that the postcondition is true following the execution of the program assuming the precondition is true

I am trying to study for a test in my programming language concepts class. I am trying to understand how to solve this problem. Our professor said we don't need to use formal notation to prove the problem as long as he can understand what we are…
yako
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What's wrong with this proof by contradiction?

Problem Consider the following proposition. What’s wrong with the following proof of the proposition? Proposition: For every real number $$, $^2≥0$. Proof: Suppose not. Then for every real number $$, $^2<0$. In particular, plugging in $x=3$ we would…
dibdub
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proof of contrapositive for square of integers

I am trying to prove the following: Prove that there do not exist integers $x$, $y$ such that $x^2 = 5y^2$. I have done the following up until now, but am unsure where to go from here: By definition, it can be seen that $x^2$ is not even. Thus,…
bawse
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Is Proof method valid

So I am studying for an upcoming midterm, and I am practicing my proofs. I found an old test online, that states the following: $| x + y | + | x − y |≥| x | + | y |, x, y∈R .$ I want to know if my proof or attempt is fair enough to prove it? my…
learnmore
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Proving that there exist infinitely many primes of the form $mn+1$.

I was wondering whether someone could tell me if the following proof is correct or help me out. Claim: $\forall n \in \mathbb{N}\colon$ there exists infinitely many primes which are congruent to $1$ modulo $n$. My strategy is using the following…
phantom
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Prove that the sum of two odd numbers is an even number.

How can I prove this? Should I take $x$ and $x+2$ or not ? I am confused.
Anna
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Show that every fraction whose square root is rational takes the form $kp^2/kq^2$.

Show that every fraction whose square root is rational takes the form $kp^2/kq^2$. What i've done: We're given that $$\sqrt{\frac{a}{b}}=\frac{p}{q}$$ Take $p/q$ as a fraction in lowest terms,then by squaring we get (assuming that $a,b$ …
Nameless
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Proof formatting for an exam

I have my very first mathematical reasoning exam tomorrow, and I'm extremely worried because our professor literally doesn't teach nor tell us anything since the class is mostly "group" work. I'm also in a Discrete Mathematics class and we prove…
Jase
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Question concerning an Argument in Paul Meyer's Book (existence of progressively measurable modification)

On the book Probability and Potentials of Paul Mayer page 69 one reads: I'm not sure how to use (1) and (2) to prove that the collection of processes is closed under sequential pointwise convergence Attempt: Let $Y_n$ be a sequence of such…
Conrado Costa
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If integers a and b are expressible in the form 4k+1 where k is a integer then ab is also expressible in the form

If integers a and b are expressible in the form $4k+1$ where k is a integer then $ab$ is also expressible in the form. This seems like a simple example But I am wondering if I did it correct. Since $a=4k+1$ and $b=4k+1$ Then…
Fernando Martinez
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Not understanding the beginning of the proof for $\log x < x$

I was reading some of the proofs for $\log x < x$ and I noticed a few of them have the proof start off with: "Let $g(x) = x - \log x$". Then they find its derivative to show if the function is increasing or not. I get that part. What I don't…
David Velasquez
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Prove: For every $\epsilon > 0$, there exists a $\delta >0$ such that $1 - \delta < x < 1 + \delta$ implies that $2 - \epsilon < 7 -5x< 2 + \epsilon$

So far this is what I have Let $$ \delta = \frac{\epsilon}{5} $$ So, if we start with $1 - \delta < x < 1 + \delta$ \begin{align} &\Rightarrow -5 + 5\delta < -5x < -5 -5\delta \quad \text{(multiply by} -5) \\ …
user3887792
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Partitioning a number as a sum of $k$ non-zero numbers, but order does not matter

I would like some confirmation regarding my logic here, which I feel is 'suspiciously straightforward'. Say I wish to express a number as the sum of $10$ non-zero numbers, where order does not matter. I can see that this is an application of the…
Trogdor
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Define the image of the function $f :\Bbb Z \times \Bbb N →\Bbb R$ given by $f(a, b) = \frac{a−4}{7b}$?

$\Bbb Z$ - integers $\Bbb N$ - natural numbers (starting from 1) $\Bbb R$ - real numbers I believe the answer is the set of real numbers ($\Bbb R$), seeing as $b$ will not equal $0$ as the set of natural numbers start from $1$. Thoughts?
Eddard
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