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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 .

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Proof-check: Proving that a rectangle of area $A$ necessarily has minimal perimeter when it is a square of side $|\sqrt A|$

Found many questions going the other way, but couldn't any like this. If I missed one, sorry. Just want to confirm if this is totally valid. Let the sides of the rectangle be $(|\sqrt A| +\alpha)$ and ($|\sqrt A|-\beta)$ with $\alpha,\beta\geq…
Rhys Hughes
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Prove a formula that gives the maximum of two numbers and uses only integer operations.

Recently I received a programming task: There are 2 numbers, you need to output the greatest, without using conditional and bit operators, without using branching and functions. Only integer operations are allowed. After some thought, I derived the…
Mouvre
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Sum of digits of $A$ + sum of digits of $B$, such that $A + B = N$

Given $N$, we have to represent $N$ = $A$ + $B$, where $A$ and $B$ are positive integers. The task is to find the minimum sum of digits of $A$ + sum of digits of $B$. For example: $N = 15$, it can be represented $A = 1, B = 14$, where the sum of…
Mohamed Magdy
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What's wrong with substituting $g(y) = 3$ into $f(z) = z^{5x + 1}$ to calculate $\frac{d\left(3^{(5x+1)}\right)}{dx}$?

I don't understand this answer, but I've rewritten it to commence with $g(y) = 3$, to avoid ambiguity. The root of the difficulty is that $x$ appears free in $f(z)$, but we are trying to "capture" it with $g(y)$, which is illegal. When…
user53259
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Composition of 3 functions

If $h:A\rightarrow B, g:B\rightarrow C, $ and $ f:B\rightarrow C$ are three functions, and $g \circ h = f \circ h$ . Is $g=h$? Initially I want to say that $g=f$. But, the proof I came up with feels incomplete. This what I got: Let $a \in A$ and $b…
WaterDrop
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Proof of even numbers

Prove that there is an infinite number of even numbers: Assume there is a largest even number, $E$. $E + 2$ would also be even, as $E$ must be divisible by 2, so $E + 2$ is divisible by $2$, and clearly greater than $E$. If $E$ is the largest even…
user634745
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Are these answers for this predicate correct?

I feel like I struggle a lot for these kinds of problems. I was wondering if someone could verify my answers and reasoning and possibly give some tips on how to solve these kinds of problems. Thank you. The problem: Alice wants to prove by…
M. Roshid
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A question on the equality between two sets.

Let $\{f_n\}_{n\in\mathbb{N}}$ a sequence of function on $X$ to $[-\infty,\infty]$ and let $\alpha\in\mathbb{R}$. I must prove that $$ \bigg\{x\in X\;\bigg|\sup_nf_n(x)>\alpha\bigg\}=\bigcup_{n=1}^\infty \big\{x\in…
Jack J.
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Proof by Induction: Summation

Hello. I am just beginning proof by induction. Would anyone be willing to see if I am grasping this correctly?
Chairman Meow
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Determine the convergence or divergence of $\sum\limits_{n =1}^{\infty} \left(n^{\frac{1}{n^2+2n+1}}-1\right) $.

Problem Determine the convergence or divergence of $\sum\limits_{n =1}^{\infty} \left(n^{\frac{1}{n^2+2n+1}}-1\right). $ Solution Notice that $$n^{\frac{1}{n^2+2n+1}}-1\leq n^{\frac{1}{n^2}}-1=\exp\left(\frac{\ln n}{n^2}\right)-1\sim \frac{\ln…
mengdie1982
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Prove that if $a,b \ge2$ such that $a^b-1$ is prime, then $a=2$

I want to start with a contradiction assuming $a$ isn't $2$ but no idea how to do that so I'm assuming it's wrong. Any help?
AnoUser1
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How can I solve this problem without using residues or Hilbert's irreducibility theorem

Let $P(x)$ be a polynomial with integer coefficients. Suppose that $P(n)$ is a $k$'th power for every integer $n$. Prove that $P(x)=(Q(x))^k$, with $Q(x)$ being a polynomial with integer coefficients. I know that this is well-known, and there are…
apple
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Modular Arithmetic Proof on getting 103 from sum of 9's and 14's only

I'm stuck on the following problem, and I will appreciate it very much if anyone could direct me with to the right way of thinking, because I currently have no idea how to proceed after the initial attempt. Question: If a store sells beers only in…
TerminatorOfTerminators
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Just using x for proving any real interval is uncountable

(newbie here) I'm trying to prove that any open real interval is uncountable. I try to proove this with a bijective function (a,b) --> R. Is there a further criteria for this than having a bijective function? If not, would it be possible to simply…
maruto
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