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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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Finding a sequence $a_{n}$ and $b_{n}$ where $a_{n}$ converges and $b_{n}$ is unbounded, and $a_{n}b_{n}$ converges

So the question is to state without proof $a_{n}$ and $b_{n}$ such that $a_{n}$ converges, $b_{n}$ is unbounded and $a_{n}b_{n}$ converges. I chose $a_{n} = \frac{1}{n}$ and $b_{n} = (-1)^n$ Then $a_{n}b_{n} = \frac{(-1)^n}{n}$ Am I correct?
mrnovice
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Find the flaw in the proof of showing diagonals of a parallelogram bisect each other.

There is something wrong with the proof of the following theorem. Find the error and correct the proof. Theorem: The diagonals of a parallelogram bisect each other. Proof: Let $ABCD$ be a parallelogram with diagonals $AC$ and $BD$ intersecting at…
Chad
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Show that $\{x\mid 0

Show that $\{x\mid 0
Garmekain
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Limit of characteristic functions being Dirac delta

So, let us have $\chi_{B(x,r)}$ , which are characteristic functions of $B(x,r)$. As limit $r \to 0$ of sets $B(x,r)$ is a point $x$, I think that a limit of $\chi_{B(x,r)}$ as $r \to 0$ should be: $f(y) = 1$, if $y = x$ and $f(y) = 0$ otherwise, or…
nikola
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How do you setup this proof?

I have the following problem and I don’t know if I’m even setting it up right. Any help is much appreciated! I’m given: Let U be any set and let P(U) be the power set of U. Prove that for every A ∈ P(U) there is a unique B ∈ P(U) such that for…
maybedave
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Can this proof be done with induction

For any natural number $x$, $x^2 + 5$ is not divisible by $4$ Or is proof by cases the only way to go about proving this?
shibu
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GCD Cases Proof Help

∀a,b ∈ N, Prime(b) ⇒ gcd(a, b) ≤ 1 ∨ gcd(a, b) ≥ b gcd(greatest common divisor) I understand this is likely cases with b divides a, and.. b doesnt divide a but am pretty lost at the moment. Can someone walk me through this step by step? thanks
shibu
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Simple domination proof

definition: Dom(f, g) : ∀n ∈ N, g(n) ≤ f(n). Let f(n) = n^2 and g(n) = n + 165. Prove that g is not dominated by f. so the negation for this question is... ∃n ∈ N, n + 165 > n^2 would you just give an example so when n =0 so.. 165>0 and you are…
shibu
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Natural deduction Tree Proof

I'm working on this: $$\dashv \lnot P \to \ (( P \to\ \lnot Q)\to\lnot P) $$ So I did this : $1\ assume \ \lnot p.\\ 2 \ assume \ p \to \lnot q.\\ 3 \ therefore \ (p \to \lnot q)\to \lnot p. \ (\to)I 2,1\\ 4 \ therefore \ \lnot p \to…
user61589
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Proof Verification: If $a\leq x_n \leq b$ for all $n\in\mathbb{N}$ and $x_n\to L$, then $a\leq L\leq b.$

I have to use the definition of convergence only to prove this. This is my attempt on proving this statement: Let $\epsilon >0$. Then, we know there is some $N\in\mathbb{N}$ such that for all $n \geq N$ we have $|x_n-L| < \epsilon$.…
user3000482
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use subtraction of the largest power of 2 to prove that each positive integer n can be expressed uniquely as a sum of distinct powers of 2.

use subtraction of the largest power of 2 to prove that each positive integer n can be expressed uniquely as a sum of distinct powers of 2. Also, what does this question have to do with binary notation? I have the main proof finished, I am…
Nicole
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Proof expectation independent discrete random variables

I have a question regarding the following theorem: Discrete random variables $X$ and $Y$ on $(\Omega,\mathcal{F},\mathbb P)$ are independent if and only if $\mathbb E(g(X)h(Y))=\mathbb E(g(X))\mathbb E(h(Y))$ for all functions $g,h\colon \mathbb…
Sha Vuklia
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Proof that ratio of products is a natural number

I have found something very interesting in my eyes. The following expression $$\frac{\prod\limits_{i=n+1}^{2n-1}i}{\prod\limits^{n-1}_{i=2}i}$$ (I think) always gives a natural number. Now, of course, I am interested in why this is so and I wanted…
Gykonik
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I reached a contradiction while proving pythagorean theorem, but I don't know what I did wrong?

By relocating the two triangles in the bottom to the top, I created the rectangle with sides $a$ and $b+b=2b$. Then, doesn't this imply that $c^2=2ab$? I am thinking that the area of four triangles add up to $c^2$ and using this fact to prove the…
user3000482
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Let $P = \{X \in \mathcal{P} (\mathbb{Z}_{+}) | X \text{ is finite}\}$. Prove that P is denumerable.

$\mathcal{P}(\mathbb{Z}_+)$ is the power set of the positive integers. I know the general way to prove a set is denumerable is to find a bijective function between that set and the positive integers, but I'm not sure how to write something that does…
IgnorantCuriosity
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