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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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Can I assume a condition in the consequent?

Im reading Axler's Linear Algebra Done Right. In an exercise, he ask to prove that $$a\in F,v\in V,av=0 \implies a=0 \lor v=0 $$ where $V$ is a vector space over the field $F$. I've proved it this way: First assume $av=0$. In order to prove that…
David Martínez
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Proof for equalities remaining

Imagine the relation x@y = z, where @ is some operation (and so is #). We often use the property that (x@y)# = z# to solve for variables. For example, $$2x = 9/2$$ We say that it will still be equal if we divide both sides by 2: $$x = 9/4$$ My math…
Jimmy360
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If a set A is bounded from above, then the set of upper bouds M has minimum

I hope the title is clear, because I am Italian and I study calculus exclusively from Italian books. I had to prove this proposition refusing to look the book (because if I read the proof, I'll forget in two hours and I don't learn). I tried this…
user3621272
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proof by contradiction

I have the following theorem: and I want to prove it by contradiction. I have started by negating the consequence, so I will have that so if I rearrange these terms I will have that: which will be against the closure property of integer numbers,…
Lila
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Let $p_n$ denote the $n$th prime and $c_n$ the $n$th composite number. Determine all positive integers $n$ such that $|p_n − c_n| = 1$.

The only ones with the property in title I could find are $n = 5$ and $n = 6$: $|11 − 10| = 1$ and $|13 − 12| = 1$. Past the $20$th prime, the list of primes grows too fast for composite numbers. Is there more general way to show this?
keys
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Let $R$ be a commutative ring with 1. If $R$ is a PID, then every prime ideal is either zero or maximal.

Let $R$ be a commutative ring with 1. If $R$ is a PID, then every prime ideal is either zero or maximal. My proof: Let $I = (p)$ be a non-zero prime ideal of $R$. Note that $p$ is prime. Since $R$ is an integral domain, $p$ is also irreducible.…
123
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Proof for $0a = 0$

Is this a valid proof for $0a =0$? I am using only Hilbert's axioms of the real numbers (for simplicity). $(a+0)(a+0) = a^2 + 0a + 0a + 0^2 = (a)(a) = a^2$ Assume that $0a$ does not equal zero. Then from $a^2 + 0a + 0a + 0^2$ we get $(a+0)(a+0) >…
Jimmy360
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Proof that $1 > 0$ using the field and order axioms

I want to prove that $1 > 0$ using the field and order axioms. So far I am trying to use the Peano axiom which states that if two numbers $n$ and $m$ have the same successor, then $n = m$. Specifically, if we have $1$ to both sides, we obtain: $$1…
user168764
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Proof by contradiction to prove an inequality does not hold

I am trying to prove that there is no positive integer x such that $2x < x^2 < 3x$. I started by assuming that this statement is true. I then subtracted 3x from each part of the inequality to get $-x < x^2-3x < 0$, for every positive integer $x$.…
user3699546
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Proving a goal with an existential quantifier and making sure it covers all cases

I'm trying to prove the following theorem: Suppose x is a real number. Prove that if x $\neq$ 1 then there is a real number y such that $\frac{y + 1}{y - 2}$ = x. The logical structure of the sentence is: x $\neq$ 1 $\implies$…
jviotti
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Proof by contradiction

I want to prove that, for all algebraic $n\neq0\text{ or }1$, $\ln n$ is transcendental. Here's how I tried to do it: $n$ is an algebraic number, $n\neq0\text{ or }1$. Assume $x$ is algebraic. $\ln n=x$ $e^x=n$ By the Lindemann-Weierstrass theorem,…
user3932000
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Proving Existence of Riemann Integral via Darboux

I am trying to prove the existence of the Riemann integral for continuous functions defined over the closed interval $[a,b].$ I am doing this with Darboux upper and lower integrals. To show that a function $f:[a,b]\to \mathbb{R}$ has a Riemann…
R R
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Verification that a statement is true or not.

Suppose that $gcd(ab,p^4) = p^3$ then $p^3 |ab$. $p$ is prime. $p^3 |ab \implies p^2|a$ and $p|b$ Is this last statement true? The converse is true i believe. EDIT. $gcd(a,p^2) = p, gcd(b,p^2) = p. $ (This is a part of a larger proof, i am trying…
user214138
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Is this proof by contradiction for the Archimedean Property correct?

I'm just starting to learn how to use proofs by contradiction, and I am just wondering if this works. Theorem (Archimedean Property): If $a$ and $b$ are any positive integers, then there exists a positive integer $n$ such that $na \geq…
user265675
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I need to prove the following proposition about natural numbers

I have the following proposition: If $p > 0$ and $mp < np$, then $m < n$. Proof: $p\in\mathbb N$. \begin{align*} np - mp \in\mathbb N\\ p\cdot(n-m) \in\mathbb N \end{align*} If $p$ and $p \cdot(n-m)$ both $\in\mathbb N$, then $(n - m) \in\mathbb N$…
Johnathan
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