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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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Mathematical induction (theory)

I've got a question about mathematical induction. $\bigg(P(0) \land \big[\forall n\in \mathbb{N},\;\; P(n)\implies P(n+1)\big]\bigg)\implies \forall n\in \mathbb{N}, \; P(n)$ for the inductive step usually we say "Let any $n\in \mathbb{N}$ and we…
Stu
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Most Important Feature from Weights

I have a dataset which I am writing a classifier for. I am using the following algorithm to calculate the $n$ weights while abs(error) < 0.5: for each example e in the training set: error = actual prediction - pred(e) update =…
lioness99a
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Consider a monotone nondecreasing function $f$ on a closed interval $[a,b].$ Show that it...

I feel as if my proof went in the wrong direction. Would someone be willing simply to verify that I've gone in the right or wrong direction, and if it is indeed the wrong direction, offer a recourse? Thank you :) (NEW TO ANALYSIS, please don't judge…
Rafael Vergnaud
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If $a \cdot a = a$ then $a=0$ or $a=1$?

If $a\cdot a = a$ then $a=0$ or $a=1$? Where $a \in \mathbb{R}.$ I try this way: Suppose that a is different to $0$ it implies the existence of multiplicative inverse: $$a^{-1}(a\cdot a)=a^{-1}\cdot a$$ $$(a^{-1}a)= 1~~~~~\text{(by…
Adrián Juárez Carrasquedo
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Assume that $\{x_n\}$ is bounded and $\lim\limits_{n \to \infty}y_n=0.$ Prove that $\lim\limits_{n \to \infty}x_ny_n=0.$

Problem Assume that $\{x_n\}$ is bounded and $\lim\limits_{n \to \infty}y_n=0.$ Prove that $\lim\limits_{n \to \infty}x_ny_n=0.$ Proof Since $\{x_n\}$ is bounded, then for all $n$ there exists $M>0$ such that $|x_n|
mengdie1982
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Justifying a common proof for the logarithmic power rule.

I need to prove the logarithmic power rule: $$\log_b(x^r) = r \cdot \log_b(x) \hspace{2.3cm}$$ I have seen a large number of sources citing a similar proof, which goes like this: \begin{align*} \text{let} \ \ m &= \log_b(x), \\ x &= b^m \\ x^r &=…
Jackie
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Proof from Axioms for a Ring

I'm trying to prove this following theorem: If $x, y \in \mathbb{Z}$, use the cancellation law for $\mathbb{Z}$ to demonstrate that $xy = 0 \implies$ $x = 0$ or $y = 0$ The proof I came up with doesn't quite seem definitive enough. I know how to…
user465188
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Are those proofs of $(-a)b = - (ab)$ and $(-a)(-b) = ab$ right?

I'm studying by Apostol and I need to proof both statements: (1): $(-a)b = -(ab)$ (2): $(-a)(-b) = ab$ My try at (1): We can rewrite $(-a)$ as $(0 -a)$ by Th 1.2(already been proved), so we can rewrite (1) as $(0 - a)b$. By Commutative Laws, we have…
Victor Feitosa
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Area of infinite number of squares inside triangle

This question is from the third sample paper for the CSAT (Computer Science Admissions Test) at Cambridge. My working is as follows: First, I worked out the equation of the diagonal line touching the top right corner of each square as being: …
Dan
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Is this proof of $0 * a = 0$ correct?

I need to prove that $0*a = a*0 = 0$ using only axiomatic properties for real numbers(It's a exercise from Apostol's book. My try: We can write $0$ as $(a - a)$. Hence we can rewrite the equation as follows: $0*a = a*0 = a*(a-a) = 0$ By distributive…
Victor Feitosa
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Is this a valid approach to solving the inequality $\frac{1}{x} < x < 1$?

I have been given the inequality $\frac{1}{x} < x < 1$ and have been told to find the values of $x$ which satisfy this inequality, and I have also been told to find these values using a case-by-case approach. I'd like to know whether my reasoning is…
Benjamin
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Request for comments on the validity of the following constructed proofs

In "Mathematical Methods for Physicists: A Comprehensive Guide, " Seventh edition, by G. B. Arfken, H. J. Weber and F. E. Harris question 1.2.13 asks the reader to show, with $n>1\,,$ that $$ \mbox{(a)}\,\,\,\, \frac{1}{n} \,\,\,\,-\,\,\,\,…
Physics_Et_Al
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Is my proof correct for $3\mid(2n^2+1) \text{ if and only if } 3 \nmid n$

I would like to know whether I have correctly proved the following result. My book gave a different proof. My concern is primarily with correctness and notation. Also, we are given: if $3 \nmid n$ then $n=3k+1$ or $n=3k+2$ and so $3\mid(n^2-1)$. $k…
Cro-Magnon
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Injective endomorphism cannot be nilpotent

Let $A$ be an injective endomorphic operator on some functions space (wlog say $C^{\infty}(\mathbb{R})$). Then it cannot be nilpotent. Does the above statement hold? I've tried to prove it like that: Proof by induction. For $n=1$, this is just…
numbertheorist
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Proof of the Uniqueness of $q$ in the Division Algorithm

I'm trying to understand a proof of the uniqueness of the quotient in the division algorithm, but the proof almost seems rather trivial to me, so it must be that I'm not understanding it. I've rewritten it somewhat. For reference, the notation…
user465188
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