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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 .

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Finding values for $n$ so that $a^n+b>n^2$

If we have $a>1$ and $a,b \in R$, what values of $n$ (which will probably be relating to $a$ and $b$) will make this inequality true? $a^n+b>n^2$ I HAD a theory that it's related to $n=max$ {${a+|b|,\frac{|b|}{a-1}}$} works but I'm having trouble…
Riley H
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Proof verification: Assume that $\forall n:x_{n}x_n.$

Problem Assume that $x_{n}x_n$$ holds for all $n=1,2,\cdots.$ Proof $\forall k \in \mathbb{N+}$,$\exists n \in \mathbb{N_+}: k
mengdie1982
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Assume that $x_1=1$ and $x_{n+1}=x_n+\dfrac{1}{x_n}.$ Prove $\lim\limits_{n \to \infty}x_n=+\infty.$

Proof First, we may prove $$x_n^2 \geq 2n-1,(n=1,2,\cdots).\tag1$$ Obviously, $(1)$ holds for $n=1$. Assume that $(1)$ holds for $n=k$, then $$x_{k+1}^2=x_k^2+2+\frac{1}{x_k^2}\geq x_k^2+2\geq 2n-1+2=2(n+1)-1,$$ which implies $(1)$ also holds for…
mengdie1982
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If $f(x)$ is derivable over $(a,b)$, then there exsits no discontinuity point of the first kind for $f'(x)$ over $(a,b)$.

Problem Assume that $f(x)$ is derivable over $(a,b)$. Prove that there exsits no discontinuity point of the first kind for $f'(x)$ over $(a,b)$. Proof Assume that $f'(x)$ has a discontinuity point of the first kind at $x=x_0$ where $x_0 \in (a,b)$.…
mengdie1982
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Is this proof form valid, where a function construction contradicts an axiom but it required that axiom to construct?

A set $N$ is defined with some axioms, where $P$ and $Q$ are two of the axioms. I am trying to prove a statement $P\rightarrow Q$ to show that $Q$ is redundant. I'm doing this by using the contrapositive. So, I assumed $\neg Q$. I defined a function…
Foon
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Proof verification for statement involving three variables

I have a statement $P(x,y,z)$ in natural numbers and I want to prove using mathematical induction and I managed to prove the following steps 1) $P(1,1,1),P(1,2,1)$ 2) $P(x,1,z)\land P(x,2,z)\land P(x,3,z)\land \cdots \land P(x,y,z) \implies…
hanugm
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Refuting the assertion that any given number can be rewritten to be undefined in a domain.

Consider the expression: $$\dfrac{(x - c_1) \cdot x}{(x - c_1)}$$ This is often simplified as $$x \ \text{for} \ x \neq c_1$$ This simplification step can also be done an arbitrary number of times for $$\dfrac{(x - c_1)(x - c_2) \dots (x - c_n)…
Jackie
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Is this proof of $ab = 0$ correct?

I have to prove the following theorem(Apostol's Calculus I, exercise 1 page 19): If $ab = 0$ then either $a = 0$ or $b = 0$. My attempt to solve it was: $ab = 0$ can be rewritten as $ab = a0$, because $a0 = 0$(already been proved). So we now can cut…
Victor Feitosa
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Prove by contradiction that a real number that is less than every positive real number cannot be positive

"Prove by contradiction that a real number that is less than every positive real number cannot be positive" [This is what I did, but it is definitely missing something... Proof: 1)Assume a real number, n, is less than every positive real and cannot…
stochasticmrfox
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proving sum of any scalar multiple of two points lie on the line passing through them

Forming the statement mathematically(And ignoring the constant C since we're taking only the x and y coordinates): Let $y = mx$ be our line Let $(x_1, y_1)$ and $(x_2, y_2)$ be the two points that satisfy the equation. Hence, we can write the…
mathmaniage
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Proof Verification For A Proof That The Domain Of An Inverse Function = Range Of Original Function

First off, let me just say that this isn't a rigorous proof. It's more like me trying to establish why the domain of the inverse function = range of the original function. Second, let me clarify what I want to establish. What I'm worried about,…
Ethan Chan
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Does $\pi$ consist of $\pi$ in it?

We do not know whether $\pi$ consists every real number in its decimals, or not. However, If we assume that $\pi$ is consisted in $\pi$ then (I think) we reach a contradiction. $\pi=\underbrace{3.14159265359...}_{n\;…
Micheal Brain Hurts
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If and A and B are separated and C is a connected subset of $A\cup B$, then either $C\subset A$ or $C\subset B$.

If and A and B are separated and C is a connected subset of $A\cup B$, then either $C\subset A$ or $C\subset B$. Proof: Suppose by contradiction that it's $\underline{not}$ the case that either $C\subset A$ or $C\subset B$, then by demorgan's law…
cemsicles
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Why does my solution only work for $|x|\le1$?

In my research, I experimented with the following set of equations: $$\sqrt{f(x)}+\sqrt{x+f(x)}=k_n$$ $$\sqrt{x+f(x)}=k_{n+1}$$ Upon solving this, it then follows that: $$\sqrt{g(x)}+\sqrt{x+g(x)}=k_{n+1}$$ $$\sqrt{x+g(x)}=k_{n+2}$$ And so forth,…
Rhys Hughes
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E.D.O - Coefficient not constant

Hello Guys i've been being difficulty to solve this Differential equation, because the coefficients aren't constant. I don't have an idea to solve. $\frac{dx}{dt}*sin(t) + x*\cos(t) = 1 , (t,x) \in (0,\pi)\times\mathbb{R}$ I'd like to find a general…
Robert Mota
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