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Questions tagged [solution-verification]

For posts looking for feedback or verification of a proposed solution. "Is my proof correct?" is too broad or missing context. Instead, the question must identify precisely which step in the proof is in doubt, and why so. This should not be the only tag for a question, and should not be used to circumvent site policies regarding duplicate questions.

This tag should be used when you have a proposed solution to a problem and have specific concerns or doubts about the validity of that solution. A question with this tag should include an explanation for why the argument presented is not convincing enough. Further discussion on using this tag can be found in the Mathematics Meta questions (1) and (2).

Answers to questions tagged look first and foremost to check that the solution is right, and to comment upon the approach taken by the author of the question. If the proposed solution is wrong, a good answer would explain where or how mistakes were made, and possibly give or sketch a correct solution instead.

If the proposed solution is correct, an answer would ideally provide further evidence to back the answerer's opinion. These could include a clearer rewriting of the given argument, alternative arguments, generalizations of the proven result, or careful consideration of unexpected subtle points. Users looking to write answers can find further discussion in this Mathematics Meta post.

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Question concerning proof of root test for series

The proof of the root test I'm reading starts with the statement: Since $ L = \lim_{n\to \infty}\sqrt[\large n]{a_n} < 1$ there exists some $L \leq r < 1$ s.t. for some $N$: $\forall n \geq N$ $\sqrt[\large n]{a_n} \leq r$ holds. But wouldn't that…
Jacob
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Prove that a monotonically increasing function is injective. Show by counterexample that a monotonically increasing function need not be surjective

Solution Verification, below is how I worked it out. I'm just wondering if I'm doing this right. A function $f:R→R$ is monotonically increasing if $ y > x $ implies $f(y)> f(x)$ for all $x$ and $y$ in $R$. Since $f(y)$ can never be less than $f(x)$…
tjblue
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Fibres of a map partition the domain

I am trying to solve the following exercise from Artin's Algebra. Prove that the nonempty fibres of a map form a partition of the domain. Here is my attempt. Let $f: A \to B$ be a map. If $A = B = \emptyset$, then the nonempty fibres of $f$, of…
user861776
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Proof Verification: If $ ( a_n ) $ is a cauchy sequence then it converges.

Theorem: If $ ( a_n ) $ is a cauchy sequence then it converges. Note: I know that the common proof of this theorem uses subsequences and the fact that if we have a cauchy sequence then it is bounded, but I first tried to prove the above theorem on…
hazelnut_116
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Is this sketch work correct way to prove?

If $$S\subseteq T\subseteq R$$ where S is non empty, then show that : if T is bounded above, then $$SupS\leqslant SupT$$. Sketch: Assume t to be supremum of T. Then $$x\leqslant t$$ for all x belonging to T. Let p be supremum of S. Then $$s\leqslant…
Natasha J
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Prove $f: \mathbb{R} \rightarrow \mathbb{Z}$ is an increasing function

Let $f$ be the following function from $\mathbb{R} \rightarrow \mathbb{Z}: f(x) = m$ where m is the unique integer such that $m \le x < m+1$. In other words, $f(x)$ is equal to the largest integer that is less than or equals to x. For instance,…
so0jong
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Prove complements

can someone help me with this problem. Notation: $A$' is the complement of A Prove that $A$ $\cap$ $B$' $\subseteq$ ($A$ $\cap$ $B$)' My work: $A$ $\cap$ $B$' = {x $|$ x $\in$ A, x $\notin$ $B$} $A$ $\cap$ $B$ = {x $|$ x $\in$ A, x $\in$ $B$} ($A$…
hanamontana
  • 333
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Truth value of statements about empty set

I have a problem: Let P be the statement " x $\in$ A and x $\in$ $\mathbb{Z}$ " Determine the truth value of statement: ($\forall$x)P $\Longrightarrow$ ($\exists$x)P Is there a set A for which the truth value of the above statement is false?…
hanamontana
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GCD proof of (m,2n)=(m+2n,n)

(m,2n)=(m+2n,n). I was testing cases before believing that this was true, and to me it only seems to be true for odd m, n, is this correct?
Joey
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How to prove this :$\left(\cfrac{1}{2}\right)! = \cfrac {\sqrt {\pi}}{2}$?

$\left(\cfrac{1}{2}\right)! = \cfrac {\sqrt {\pi}}{2}$ I saw this in a math book. I tried to prove it but I'm unable to. Any hints or solutions would be most appreciated.
user880107
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Proof check $f(x)=\frac{2x}{x-4}$ diverges as $x\to4$ using $\epsilon-\delta$

My nephew asked me to consider $\lim_\limits{x\to 4 }\left(\frac{2x}{x-4}\right)$ for a problem set he was doing. I explained that it diverged by substituting $x=4+\delta$ and letting $\delta\to 0$. I thought I'd try to do it formally using…
Karl
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Confirmation on Proofs

Q1: Suppose $(x_n)$ satisfies $-1$ $\leq$ $x_n$ $\leq$ $1$ for all $n$ $\in$ $\Bbb{N}$. Suppose $(x_{n_k})$ is a subsequence of $(x_n)$ converging to $(x_0$) $\in$ $\Bbb{R}$. Prove that it is always true that $-1$ $\leq$ $x_0$ $\leq$ $1$ Just for…
Sam Connell
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Finding mistake in the proof regarding a prime test

My proof is: Let $N=pq$. If $p=k\sqrt{N}$ where $k\in\mathbb{Q}^+$, then $q=\dfrac{\sqrt{N}}{k}$. If $k=1$, clearly $\sqrt{N}$ is a factor of $N$. If $k<1$, then $p<\sqrt{N}$, so there must be at least one factor of $N$ less than…
ultralegend5385
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If the product $x_1x_2 ··· x_n$ is zero, then $x_1$ and $x_n$ are zero, is this statement true

Let $n$ be a natural number greater 1 and let $x_1, x_2,..., x_n$ be real numbers. Consider the following statement. If the product $x_1x_2 ··· x_n$ is zero, then $x_1$ and $x_n$ are zero I'm pretty sure that this statement is not true, since as…
mathyman
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Show by mathematical induction that if $n$ is a positive integer, then $(2n)!\lt 2^{2n}(n!)^{2}.$

I want a proof verification. Prove that $$\boxed{ n\in \mathbb{Z}^{+} \Rightarrow (2n)!\lt 2^{2n}(n!)^{2}}$$ by mathematical induction. Since $n=1$ implies that $(2\cdot 1)!=2\lt 2^{2\cdot 1}\cdot (1!)^2=2^{2}\cdot 1=4$ the base case holds. Assume…
Victor Galeano
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