Questions tagged [solution-verification]
For posts looking for feedback or verification of a proposed solution. "Is this proof correct?" or "where is the mistake?" 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 duplication.
46,219 questions
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Showing that $\nexists r \in \mathbb{Q} : 2^r=3$
I am currently self studying real analysis from the book Understanding Analysis, Stephen Abbott, 2nd edition. In page 11, exercise 1.2.2 the problem asks to show that there is no rational $r$ ...
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Under what conditions does $\overline{(a,b)}=[a,b]$ hold? ("Topology Second Edition" by James R. Munkres.)
I am reading Topology Second Edition by James R. Munkres.
Exercise 5 in Section 17 in this book:
Let $X$ be an ordered set in the order topology. Show that $\overline{(a,b)}\subset[a,b]$. Under what ...
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If $H$ and $N$ are respectively a pronormal and normal subgroup then is $H\cap N$ pronormal in $N$?
If $H$ is a subgroup of a group $(G,\ast,e)$ then it is said pronormal iff for any $g$ in $G$ there exists $x$ in $\left\langle H\cup(g\ast H\ast g^{-1})\right\rangle$ such that the equality
$$
g\ast ...
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Is this a valid proof that $\displaystyle \lim_{x\rightarrow\infty}\frac{1}{x^2}=0$? [closed]
I know that the limit can be proven using the standard $\varepsilon$-$\delta$ definition of limits but is my proof valid? If not, what is it lacking and how is it flawed? Below is my approach to the ...
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Generalisation of the inequality $D.C\geq\operatorname{mult}_x(D)\cdot\operatorname{mult}_x(C)$.
Let $X$ be a smooth projective variety of dimension $n$ over an algebraically closed field, $x\in X$ a closed point, $C\subset X$ an integral curve containing $x$, $Y\subset X$ a prime divisor ...
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Help Revising a 2-Column Proof for Euclid's Elements I.7
This is my working 2-column proof for Book 1 Proposition 7. I would be remiss in saying that this is completely foolproof. One question is how we are to formulate a proof by contradiction within the ...
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Let $a$ be a digit. When the number $25!$ is divided by $23!-a$, the remainder is $60^2$. Determine the value of $a$. [duplicate]
Let $a$ be a digit ($a\in{0,1,\dots,9}$). When the number $25!$ is divided by $23!-a$, the remainder is $60^2$. Determine the value of $a$ .
I want to know how rigorous my solution is. Is there ...
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Base change of modules and the group of homomorphisms
Let $A,B$ be commutative rings and in particular, $B$ is an $A$-algebra defined by a homomorphism $f:A \to B$. I want to prove that the following three conditions are equivalent.
$B \otimes_A B\cong ...
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If $H$, $K$ and $L$ are subgroup such that $H$ commutes with $K$ and $L$ then is $H\ast K\ast L$ a subgroup?
If $H$ and $K$ are subgroup of a group $(G,\ast,e)$ then I know that $H\ast K$ is a subgroup of when $H$ is commutable with $K$: so I am searching a counterexample showing that if a subgroup $X$ ...
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How $1+2+3+...+n\mid 1^k+...+n^k$ for all odd $k$ for $n \in \mathbb{N}$? [duplicate]
How $1+2+3+...+n\mid 1^k+...+n^k$ for all odd $k$ for $n \in \mathbb{N}$?
The proof (Pathfinder) requires using no more than EDL. I found no source. About trying, I can't find where to begin with.
Is ...
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Is my Euclidean-style proof valid? It is for a summation of infinitely many line segments equaling to a finite length without calculus, or limits. [closed]
I have attempted to prove that the sum of infinitely many quanities can still equal a finite quantity without using calculus, measure theory, or any other modern mathematical tool such as set theory.
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Minimum cardinality of the set of values for a sequence($a_1,a_2...a_{2025}$) with distinct cyclic ratios
Let $n = 2025$. We are given a sequence of positive integers $a_1, a_2, \dots, a_n$.
Let the cyclic ratios be defined as:
$$r_i = \frac{a_i}{a_{i+1}} \quad \text{for } 1 \le i \le n-1, \quad \text{and}...
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How to solve $ \lim\limits_{x\to+\infty} \!\!\left(\! \frac{x^{2}+3}{3x^{2}+1}\! \right)^{\!x^{2}}\!\!\!=0\;?$
I know it can be solved with Squeeze's theorem, but I want to verify that this more conventional method might also be valid.
$$ \lim_{x\to+\infty} \left(\frac{1+\frac{3}{x^{2}}}{1+\frac{1}{3x^{2}}}\...
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'Almost uniformly Lipschitz' implies uniformly equicontinuous
Suppose a sequence of functions $\{f_i\}_{i\ge 1}$ in $C(B_1)$ (continuous in the unit ball in $\mathbb R^n$, $n\ge 2$) are 'almost uniformly Lipschitz' in the following sense:
there exists a ...
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Proving a Claim about four mutually tangent unit spheres
Prove the Claim about four mutually tangent unit spheres :
(1) The centers of each sphere lie at the vertices of a regular tetrahedron of edge length $2$
(2) Their points of tangency lie at the ...
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