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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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If $gf$ is 1-1, is $g$ 1-1?

Suppose $gf$ is 1-1. Is $g$ 1-1? Let $g(f(x_0)) = g(f(x_1))$. Then $x_0 = x_1$. Then $f(x_0) = f(x_1)$. So $g$ is 1-1. Maybe there might not exist an $x_0$ or an $x_1$, but I assume since $gf$ is 1-1, then an $x$ must exist. So I wouldn't need to…
Don Larynx
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Determining if two things are equal when they contain a floor function

I have two equations: $ 50.8 \lfloor \frac{w - 1}{50.8} \rfloor $ and $ 25.4 \lfloor \frac{w - 1}{25.4} \rfloor $ I need to determine if they are equal, how can I do this? What I think the the first equation does is determine the nearest width to…
Lerp
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Archimedean property application with logarithms

I am attempting this proof but do not know what to do about assuming the sign of $a$. Is this proof correct?I don't think it is because the result is supposed to hold for all $a$ The problem is prove if $a \in \mathbb{R}$,$\exists n \in \mathbb{N}$…
user707991
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Prove that $19\vert 2^{2^{6k+2}}+3$ for every $k=0,1,2,3,\cdots$.

Can someone please verify (or falisfy) the following proof of the statement in the title. Proof. Consider $$19\vert 2^{2^{6k+2}}+3.$$ $19$ divides this sum if and only if $$16\vert 2^{2^{6k+2}}$$ since $2^{2^{6k+2}}\equiv 16~mod~19$ and $3\equiv…
Victor Galeano
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Test for Primality Proof

For this problem, you are provided with the following definition: "A Test for Primality is the following: Given an integer n > 1, to test whether n is prime check to see if it is divisible by a prime number less than or equal to its square root. If…
user724190
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2 answers

Equivalent Proofs?

Is proving both: For all natural numbers n, if n is a perfect square, then the root of n is not irrational. For all natural numbers n, if the root of n is irrational, then n is not a perfect square. The same as proving: For all natural numbers n,…
user724190
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LDA proof that maximizing logarithm is the same

In "An introduction to Statistical Learning with Applications in R" on page 139, section 4.4.2, we have that $$ p_k (x) = \frac{\pi_k f_k (x)}{\sum_{l=1}^K \pi_l f_l(x)} $$ If we assume that $f_k(x) \in N(\mu_k, \sigma_k^2)$, and further we assume…
armara
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Logic of proof: vacuously true

In a proof, I defined a term, say T, if a subobject of class of objects however the subobject may not exist in general. Do objects , which do not have the subject, still classify as T? I think it should still as it follows the logic of the empty set…
kishan17
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Show that $L:= [ { (x,y,z) \in R^3 : x^2 + y^2 + z^2 −2xy−2yz + 2xz = 0}] $ is a sub vector space

Show that $L:= [{ (x,y,z) \in R^3 : x^2 + y^2 + z^2 −2xy−2yz + 2xz =0 }] $ is a sub vector space of $R^3$ Proof: 1) show it is not empty (0,0,0) is inside thus not empty. 2) Scalar multiplication with $\lambda \in K$ multiplied $(x_1,x_2,x_3)\in L$…
Mad
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Proof of reflexive property of equality. Is it correct?

We can assume that for every $a, a=x$, in which $x$ is anything including nothing or something. If $a\neq x$ then $a$ doesn't exist. $a=x$ given $x=a$ symmetry $a=a$ transitive
Ron Davidov
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Proof if two planes intersect in more than one line they are identical

Good afternoon, I am trying to prove that if two planes intersect in more than one line, then they are identical: Planes $P_1$ and $P_2$ intersect at $l_1$ and $l_2$. By the definition of a line $l_1$ contains $\alpha$ and $\beta$ and $l_2$…
Yar
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Proving $1^3+ \cdots + n^3 = (1 + \cdots + n)^2$ by induction

I'm currently working on problems in Spivak's Calculus and just wanted to make sure that I have the right idea here. In Chapter 2, Problem 1, we are told to prove the following formula: $$1^3+ \cdots + n^3 = (1 + \cdots + n)^2$$ Here is what I…
user716234
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to show that class $\mathbb S$ is preserved under square-root transformation, i.e. $g(z)=\sqrt{f(z^2)} \in \mathbb S$

$\mathbb D$={${z \in \mathbb C / \mid z \mid < 1 }$} $\mathbb S$ be the class of all functions $f$ on $\mathbb D$ such that $f$ is univalent (analytic + injective) and $f(0)=0$,$f'(0)=1$. I want to show that class $\mathbb S$ is preserved under…
ogirkar
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Law of exponent proof

How can I proof In a two column table that $\left(\frac{a}{b}\right)^n= \frac{a^n}{b^n}$ given $n$ is any positive integer.
eniid15
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Prove that consecutive integers are always coprime

I'm wondering if the proof below is strong enough to prove that consecutive integers are always coprime. Let $a$ and $(a+1)$ be our $2$ numbers, and suppose $a$ has $k$ that divides it, then we have $a\equiv 0 \bmod(k)$ , and adding $1$ to each side…
john fowles
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