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.

21426 questions
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Is my induction proof correct?

Prove: $\forall n,m\in \mathbb{N_{0}}:n+m\in \mathbb{N_{0}}$. Remark. By $\mathbb{N_{0}}$ we mean $0\in \mathbb{N}$. Proof. Let $n,m\in \mathbb{N_{0}.}$ Providing $m=n=0,$ \begin{align*} n+m=n\tag*{because $n+0:=n$} \end{align*} Thus $n\in…
user923938
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A Proof of the Formula for the nth Triangle Number

The triangle numbers are 1,3,6,10,etc... The nth triangle number is formed by the following sum: $T_n=\sum_{i=1}^n i=1+2+3+...+n$. I want to try and derive the general formula for the nth triangle number in the following manner. Form a rectangle…
X Stanton
  • 419
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How to prove $A$=$C$-$B$ with given hypotheses?

Hypotheses: $A$ ⊆ $C$, $B$ ⊆ $C$, $A$ ∪ $B$ = $C$ and $A$ ∩ $B$ = ∅ Proof: Let $x ∈ A ⇒ x ∈ C ⇔ x ∈ A ∪ B.$ Since $x ∈ A ∧ x ∈ A ∪ B ∧ x ∉ A ∩ B ⇒ x ∉ B.$ Since $x ∈ C ∧ x ∉ B ⇒ x ∈ C - B.$ Let $x ∈ C - B ⇔ x ∈ C ∧ x ∉ B ⇒ x ∈ C ⇔ x ∈ A ∪…
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Prove that $\forall$x$\in$Z, $[16|x^3]$ $\Rightarrow$ $[2|x]$

Claim: $\forall$x$\in$Z, $[16|x^3]$ $\Rightarrow$ $[2|x]$ Also provide a counterexample which disproves the converse. My attempt Proof. Suppose $16|x^3$. Then $x^3=16q$, where $q\in$$Z$. Taking the cube root of both sides of the eqn. $x^3=16q$ gives…
Karam
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Schröder Bernstein Proof

I'm trying to. understand the proof in Halmos's book of the Schröder-Bernstein theorem. Here is my best attempt to replicate it. Statement: If there exist injections $f: X \to Y$ and $g: Y \to X$, then there is a bijection $h: X \to Y$. Let $f: X…
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Proof Verification:$\lim\limits_{n\to \infty} a_n=- \infty $ and $ \lim\limits_{n\to \infty}b_n = b <0 $, show $ a_n b_n \longrightarrow +\infty $

Problem: Given that $ \lim\limits_{n \to \infty} a_n = - \infty $ and $ \lim\limits_{n \to \infty} b_n = b <0 $, show $ a_n b_n \longrightarrow +\infty $ Note: there's an answer to the problem here Prove that $\lim\limits_{n\rightarrow…
hazelnut_116
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Is this correct way to find this limit?

I have to find limit of the following $(a^\sqrt{x}-a^\frac{1}{\sqrt{x}})/(a^\sqrt{x}+a^\frac{1}{\sqrt{x}})\;$ as $x$ tends to $0$. My attempt: $(a^\frac{x-1}{\sqrt{x}}-1)/(a^\frac{x-1}{\sqrt{x}}+1)$ Now let $\frac{x-1}{\sqrt{x}}=t$ Then as $x$ tends…
Natasha J
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What is the form of the normalizing constant of the continuous categorical distribution when two or more parameters are equal?

In the paper "The continuous categorical: a novel simplex-valued exponential family", the supplementary material shows that the normalizing constant of the continuous categorical density function can be written…
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Prove that for every positive real number $\epsilon$, there exists a natural number $N$ such that if $n > N$, then $\frac{1}{n^2+1} < \epsilon$.

Initially, I had: Let $N$ be an arbitrary natural number and $n > N$. Assume $N < \sqrt{\frac{1}{\epsilon}-1}$. Since $n > N$, $n > \sqrt{\frac{1}{\epsilon}-1}$. Therefore, $ n > \sqrt{\frac{1}{\epsilon}-1}$, then $ n^2 > \frac{1}{\epsilon}-1$ ,…
red
  • 309
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Prove some set in $(l^\infty,d_\infty)$ is closed.

Can someone verify if my reasoning is ok? After parsing the definitions, I realized that I need to show that if I let $x \in \bar A$, the closure, then $x \in A$ to show closed, which is same as proving $n\vert x_n\vert \leq 1$ for all $n\geq…
nabu1227
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Write the definition of prime number using symbols and no words

I'm trying to write the definition of prime numbers using only symbols. Here is what I have: A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. Note: N$^{*}$ is the set of all natural…
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Verification of my proof for irrationality of $\sqrt2$

Here's my proof: Let us suppose for sake of contradiction, $\sqrt2$ is rational. Then, we can write $$\sqrt2=\frac{a}{b}$$ for non-zero coprime integers $a$ and $b$. Squaring our equation, $$2=\frac{a^2}{b^2}$$ Here, LHS is an integer, but since…
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Proving that there is a unique real number x such that for every real number $y$, $xy+x-4=4y$

The question is from problem 2 of chapter 3.6 of Velleman's How To Prove It (2nd edition). The question has been asked by another user before, but I couldn't find any thread that addresses the specific problem I have with my proof/problem. My…
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Proof that the set of all bijective functions over the natural numbers is uncountable.

Problem: Prove that the set of all bijective functions over the natural numbers is uncountable. I have already seen a lot of answers to this problem and there seems to be always a part where the natural numbers are partitioned into two countable…