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.
46,210 questions
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How 1$+2+3+...+n|1^k+...+n^k$ for all odd $k$ for $n \in \mathbb{N}$ [duplicate]
The proof (Pathfinder) requires using no more than EDL. I found no source. About trying, I can't find where to begin with.
Is this bound to be beyond EDL? (EDL is the topic that covers this question ...
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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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Is this constructive method for determining the minimal ε–index of a convergent sequence already known?(Osamah banat theorem for determine least index [closed]
I am studying the ε–definition of convergence for real sequences.
Classical textbooks state that for every , there exists an integer such that
$$|a_n - L| < \varepsilon \quad \text{for all } n \ge ...
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Minimum cardinality of the set of values for a sequence($a_1,a_2...a_{2025}$) with distinct cyclic ratios
Let $n = 2025$. We are given a sequence of positive integers $a_1, a_2, \dots, a_n$.
Let the cyclic ratios be defined as:
$$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 ...
- 12k
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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 ...
- 6,461
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Does $C \cong \left( B / A \right)$ imply the existence of a short exact sequence $0 \to A \to B \to C \to 0$
Throughout the whole post $R$ is commutative with unity, and $A,B,C$ are $R$-modules.I'm currently taking my first course in commutative algebra, and I'm trying to get a better feel for how short ...
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Proving that the set of the quotients of Fibonacci numbers is not dense in the positive reals
As in the heading, I'm trying to write up a proof that the quotients of all Fibonacci numbers is not dense in $\mathbb{R_+}$. This is what I have come up with and would like to know if it's correct.
...
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The least positive integer ending in $7$ which quintuples if the $7$ is moved to the front
I wrote up an attempt at the first problem in "Problem Primer for Olympiad," which is:
Find the least number whose last digit is $7$ and which becomes $5$ times larger when this last digit ...
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1
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Show that $w\in W$ if and only if $w\wedge w_1\wedge\cdots\wedge w_k = 0$ in $\wedge^{k+1}V$
Let $w_1,\dots,w_k$ be linearly independent and $W=\mathrm{span}\{w_1,\dots,w_k\}$.
If $w\in W$, then
$$
w = a_1 w_1 + \cdots + a_k w_k
$$
for some scalars $a_i$, then $\{w,w_1,\dots,w_k\}$ is l.d. ...
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Property Preserved by Invertible $\mathbb{R}$-Linear Homeomorphisms Between Topological Vector Spaces over the Reals.
Please see Folland's second edition of Real Analysis, Modern Techniques and Their Applications or Wikipedia's Topological Vector Spaces for the definition of a Topological Vector Space over $\mathbb{R}...
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$f(0)=1$, $f(x) \ge 0 \ge f'(x)$, $f''(x)\le f(x)$ for $x\ge 0$
Problem
Let $f$ be a twice differentiable function on the open interval $(-1,1)$ such that $f(0)=1$. Suppose $f$ also satisfies $f(x) \ge 0, f'(x) \le 0$ and $f''(x) \le f(x)$, for all $x\ge 0$. Show ...
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Arrangements of 10 Balls Chosen from Red and Blue, Where Every Blue Ball Has a Blue Neighbor(need pure combinatorics solution)
Question
Consider a linear arrangement of $10$ balls selected from an infinite supply of blue and red balls.
Determine the total number of distinct arrangements that satisfy the following condition:
...
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Is the isomorphism $(G/N_1)/(N_2/N_1)\cong G/N_2$ in the third isomorphism theorem actually an equality?
I tried to understand the concept that, for a group $G$ and two normal subgroups $N_1,N_2$ with $N_1\subseteq N_2$ it holds that
$$(G/N_1)/(N_2/N_1)\cong G/N_2,$$
but my following reasoning seems to ...
