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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 there do not exist three distinct real number a,b and c such that all of the numbers a + b + c, ab, ac, bc, abc are equal.

Can you guys tell me if this is right? Assume, to the contrary, there exist three distinct real number a,b and c such that all of the numbers a + b + c, ab, ac, bc, abc are equal. Then $4(a+b+c)=abc + ab + ac + bc$. Since, $a(4-b) + b(4-c) + c(4-a)…
user562302
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The validity of my proof for the following statement: for any integer $n$ larger than $0$, prove that if $a^n$ is even, $a$ has to be even as well

I know that this is a trivial question, but I have never done any serious proofs before and therefore I am a complete novice when it comes to that part of math. Anyhow, I used the "prove by contradiction" technique and my proof is the…
Luka Duranovic
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How to prove that for index $i$ all the following $n$ sums are negative?

Given are $n$ real numbers $x(1), x(2), ..., x(n)$. Some of them are negative, some may be positive. The total sum is negative. Prove the following statement: There exists some index $i$ such that all the following $n$ sums are…
Abd El-Rahman Ahmed
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In this situation, is there a relation between x and y that is always true regardless of the values of the other variables involved?

The situation: $$x=\frac ab\quad \& \quad y=\frac a{b+c}$$ (Image here, won't allow me to post images because of my low reputation)
Raylight
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Constructing an increasing sequence of numbers from a set

I have an infinite set $A$ of real numbers and I wish to construct a strictly increasing sequence using elements of $A$. This is what came to my mind - Pick any element from $A$ and name it $a_1$. Pick a different element from $A$. If this is…
Not Euler
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Is there a proof that $2^x - 3^y$ is always increasing?

Quite new here and after researching I haven't seen the thing I was looking for. Also, my apologies if I use wrong math variables, I am an enthusiast, not a professional. The question is: For x= 1 to infinity and y = 1 to infinity, "in $2^x - 3^y =…
RobinvG
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Question on proofs of limits

If I am trying to prove a limit say $\lim(5x-3)=2$ as $x\to1$ then Let $\epsilon$ be given. the aim is to find a $\delta>0$ such that whenever $0<|x-1|<\delta$ then $|f(x)-2|<\epsilon$ My question is if I work from $|f(x)-2|<\epsilon$ to isolate $x$…
Carlos Bacca
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Proof by contradiction to show two equations are not equal

I apologize for the terrible formatting. I'm reading the guide and trying stuff out but its not working. Extremely sorry, but please bear with me. Prove the following: If $x$ and $y$ are positive real numbers then $(x + y)^2 \neq x^2 + y^2$ I…
wantToLearn
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Is this a valid proof for the general Leibniz rule?

I want to prove the following formula by induction: $$\sum_{k=0}^n \begin{pmatrix}n \\ k\end{pmatrix} f^{(k)}g^{(n-k)}$$ The base case is trivial but I am not sure if my reasoning is valid for the inductive step. Here is what I have got so…
qmd
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Proof: n can be written as the sum of a nonnegative multiple of 4 and a nonnegative multiple of 5.

I am trying to prove this statement, but am having some trouble with it. I think I am in the right direction but would like some feedback. Note: The proof must be completed using induction, and it looks like I need strong induction. For every…
Minatorr
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Left and Right inverse of a function

My proof is attached in the picture.
Hello
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Why is this argument valid? Velleman

Why is the pictured argument valid? Velleman in this chapter section says that an argument is valid only if the conclusion has the option of not being true if all the premises are true. But row 7 is the only row where all three premises (Premise 1…
user152810
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direct proof - prove the inequality

[I have proved a similar inequality; here.][1] I am trying to prove the inequality: $$x + \frac 1x \le -2, x < 0$$ I can proceed like I did in [1]. Scratch work; like so: $$x + \frac 1x \le -2$$ $$ x(x + \frac 1x) \le -2x$$ $$ x^2 + 1 \le 2x$$ $$…
Job H
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Is this a correct proof of the Pythagorean theorem?

I had an idea for a proof by contradiction of the Pythagorean theorem. Where the angle between the base, x and the hypotenuse z is $\theta$, of a right angled triangle. And the side opposite to the angle is y. Assume that $$x^2 + y^2 \neq z^2$$ Then…
benjamincantor
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Prove proposition on integers using axioms

How can I prove: If $0 < a$ and $0 < b$, then a < b if and only if $a^2
F. Zer
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