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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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Suppose $a$ is a perfect square and $a \ge 9$. Prove that $a - 1$ is composite.

Let $a = x^2$ since $a$ is a perfect square. Then $a - 1 = x^2 - 1$. Claim: $1 < x + 1 < x^2 - 1$. Since $x^2 \ge 9$, $x \ge 3$. Since $x \ge 3$, $1 < x - 1$. Multiply both sides of $1 < x - 1$ by $x + 1$: $x + 1 < x^2 - 1$. Since $1 < x + 1 < x^2…
VladimirPutin
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Integrability condition on the Fourier transform

I have a question for This is much healthier who answer my query- This is a problem from the book from Stephane Mallat "A wavelet Tour of signal processing: a sparse way". A function $f$ is bounded and $p$ times continuously differentiable with…
SAMEER
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Proof of conjugate verification.

Prove $\frac{z_1}{z_2} = \frac{\overline{z_1}}{\overline{z_2}}$ if $z_2\neq0$. Proof: Let $z_1=a_1+ib_1$ and let $z_2=a_2+ib_2$, where $a_1, b_1, a_2, b_2 \in \Re$. $$\frac{z_1}{z_2} =…
Michelle
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What is effective price of suger

The price of sugar was Rs$25.00$ on January. It got increased in February by 40%. In March the price was reduced by 40%. The new price will be: My solution: $25[1+0.4][1-0.4]=21$ Is it correct?
Syn
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Proof of integral test

$f:[1,\infty)\rightarrow \mathbb{R}$ monotone decreasing and $f(x)\ge 0$ and $\int_1^{\infty} f(x) dx$ exists $\Rightarrow$ $\sum_{n=1}^{\infty} f(n)$ is convergent I need to prove this statement with these marks. I know that $\sum_{k=2}^n f(k) \le…
user128576
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Looking for an error in a simple proof

Assume n is an integer. If the square root of $n$ is rational, prove that $n$ is a perfect square. To prove the above statement, I used a trick rather than the standard way of using the unique factorization theorem over the field of integers. My…
user135562
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Bijective operator has dense image

Let $T\colon C[0,1]\to C[0,1]$ be a bijective operator. My (maybe silly) question is if $T$ then has a dense image. I think I can show this in general: Let $f\colon X\to Y$ be bijective. Consider any $y\in Y$. Then there is exactly one $x\in X$ with…
user34632
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Simple inequality, proof

There is a following inequality $$\frac{x_{1}^{2}+x_{2}^{2}+...+x_{n}^{2}}{n}\geq\frac{x_{1}^{2}+x_{2}^{2}+...+x_{n}^{2}+2x_{1}x_{2}+...+2x_{1}x_{n}+2x_{2}x_{3}+...+2x_{2}x_{n}+...+2x_{n-1}x_{n}}{n^{2}}.$$ In my opinion, it is held for all $x_i>0$.…
tomb
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Clarification of the proof of a theorem: Triangle inequality

First: My proof of the triangle inequality: If $a,b \in \mathbb{R}$, then $|a+b| \leq |a| + |b|$ Proof: Consider the 4 cases: 1) $a<0$ and $b<0$ 2) $a>0$ and $b<0$ 3) $a>0$ and $b>0$ 4) $a<0$ and $b>0$ $$1. |-a - b| \leq |-a| + |-b| = |a| +…
Display Name
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One-to-one and Onto: True or False

1) Suppose ${f}: X\to Y$ is one-to-one and $A\subseteq X$. Then $f^{-1}({f}(A))=A$. True 2) Suppose ${f}: X \to X$, and assume that ${f} \circ {f}$ is one-to-one and onto. Then ${f}$ is one-to-one and onto. True 3) Suppose ${f}:X\to Y$ is a…
Vincent
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Proof by contradiction:$E_1 +E_2\doteq E_1\oplus E_2\leftrightarrow \forall x \in E_1+E_2(\exists! e_1 \in E_1,e_2 \in E_2(x=e_1+e_2))$

I must by contradiction: let $E_1,E_2$ two vector subspacesof $V$, then: $$E_1 + E_2\doteq E_1 \oplus E_2 \leftrightarrow \forall x \in E_1+E_2(\exists! e_1 \in E_1,e_2 \in E_2(x=e_1+e_2))$$ I must show: $$1)E_1 + E_2\doteq E_1 \oplus E_2 \to…
mle
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Is $(B-C) = B\cap\overline{C}$ a set equivalence rule?

I have to prove the following using set equivalence rules. $A\cap(B-C) = (A - B) \cap(A - C)$ I can only use the Distributivity law with AND and OR as far as I can tell. I think I can go ahead with the proof if I can assume that $(B-C) =…
MrX
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Can the fact $(\sin x)'=\cos x$ be proved not using the fact $\lim_{x\to 0} \frac{\sin x}{x}=1$?

Is it possible to prove $$\left(\sin(x)\right)^\prime = \cos(x)$$ without using the fact that $\displaystyle\lim_{x\to 0} \frac{\sin x}{x}=1$? If so, Please give me the proof of that case.
ElectronicKid
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Proof of $1^2+2^2+\cdots+n^2=n^3/3+n^2/2+n/6$

I'm having a difficulty understanding this It's only the addition part which I'm not following. From what I've understood: If we have a certain number of formulas and we add them, this is what happens on the left side: $$3\cdot 1^2+3\cdot…
user108343
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Counter examples to inscribed squares conjecture

Can the counter examples found by me qualify as a counter proof for the "inscribed squares problem" (the Toeplitz' conjecture) ? I ask this here because the problem stands as unsolved for 100 years, and the counterexamples below appear too simple.…
Mihai Cirneala
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