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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If for each $a \in X$ and each $r > 0,\, \{F(x): ||x-a|| < r \} = \mathbb{R}$ , then $F$ is unbounded.

Let $X$ be a normed linear space and let $F$ be a linear functional defined on $X$. Prove that $F$ is unbounded if and only if for each $a \in X$ and each $r > 0,\, \{F(x): \|x-a\| < r \} = \mathbb{R}$. I am particularly interested in one…
Emptymind
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Finding a closed expression solution for an equation

Have been dealing with this equation for a while, but yet able to get a simple expression. I have already done numerical solution and seems to be working just fine, but I would like to get a closed expression. The problem is to find $x$ form the…
kentropy
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How sufficient is this proof for the inverse of an inverse being the identity relation?

I was studying mathematical analysis with the book Introduction to Mathematical Analysis (Parzynski and Zipse, 1987) and had a question regarding an exercise problem. It's actually the same one as this question but I was curious if my approach was…
Sean
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very basic verification of pre-image of a function

working with the set $\{(1,2),(2,1),(3,1),(5,4)\}$ I always second guess myself and sometimes confuse myself over simple things. The question asks whats the pre-image of $f^{-1}(1)$. My answer is that the pre-image is $(2,3)$ since $2,3$ in domain…
K. Gibson
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Proof of Infinitely Many Odd Numbers

Is this a valid proof of infinitely many odd integers? Assume, to the contrary, that there are finitely many odd integers. Let $S$ be the set of all positive odd integers and let $x=\sum_{n\in S} n$. Then, $|S|$ is even or $|S|$ is odd. Let $|S|$…
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Find all triples of non-negative real numbers (a,b,c)

Find all triples of non-negative real numbers (a,b,c) which satisfy the following set of equations: $ \begin{cases} a^2+ab=c\\ b^2+bc=a\\ c^2+ca=b\\ \end{cases}$ My Attemp: Solution: The only solutions in non-negative numbers of the system of…
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Prove/Disprove that $B \subset f(f^{-1}(B))$

$f:X \rightarrow Y$ where $A \subset X$ and $B \subset Y$ Prove (if it is correct) that $$B \subset f(f^{-1}(B))$$ This is my approach Proof Choose an arbitrary element $y \in B$, by the definition of inverse image, we know that $x \in f^{-1}(B)$…
NimaJan
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Prove that $\exists y \in \mathbb{R}: \forall x \in \mathbb{R} : x+y =0$ is not correct

Prove that the following statement is not correct $$\exists y \in \mathbb{R}: \forall x \in \mathbb{R} : x+y =0$$ I have difficulties proving this. I think that the best value $y$ can have is to be equal to $-x$. So I can give a contradiction by…
NimaJan
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Prove $m^3 \leq 2^m$ for $m \geq 10$ with induction

Prove that $m^3 \leq 2^m$ for $m \geq 10$ This is my shot Proof We prove this by induction. Basic step: For $n=10$ is $10^3 \leq 2^{10} = 1000 \leq 1024$ and that is correct. Induction step: Assume that $k \geq 10$ and that the statement is true for…
NimaJan
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Prove that for any integers x and y and any integer k that if $x \equiv_k y$, then $y \equiv_k x$.

If anyone has a better method please feel free to comment it below. My proof: This is a direct proof. Assume $x \equiv_k y$ is true. From $x \equiv_k y$ we know that: x = y + kq, where q is q ∈ Z $\space\space\space\space\space\space$ (1) Now if…
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Is this a correct way of proving that $|A|<|P(A)|$ for infinite sets?

In this video on PBS Infinite Series, they attempt to prove: $$|A| < |\mathcal{P}(A)| \tag{1}$$ Where $A$ is a set (possibly infinite), $|A|$ is the cardinality of $A$ and $\mathcal{P}(A)$ is the power set of A. They use the following…
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If $q$ is prime, then does the following inequality have any solutions for an integer $k > 1$?

Good day! If $q$ is prime, then does the following inequality have any solutions for an integer $k > 1$? $$\frac{q + 3}{q} \leq \frac{q^{k+1} - 1}{q^k(q - 1)}$$ Here is my attempt: $${q^k}(q^2 + 2q - 3) = {q^k}(q - 1)(q + 3) \leq q(q^{k+1} - 1) =…
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Splitting equation into two pieces

I am working through a book I just bought, and got stuck a bit. The book uses a string of substitutions to transform an equation to one easier. So the final equation is this: $T \cdot o - P \cdot o + T \cdot d - P \cdot d = f - a$ I substituted…
nutship
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Contradiction proofs and proof by cases

I haven't really found a solution to this confusion I currently have. I know in certain cases, we can use "without loss of generality" to proceed in a proof. For example, to prove that "if a|b or a|c -> a|bc", we can assume without loss of…
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If $a,b$ are two distinct real numbers, then either $\frac{a+b}{2}>a$ or $\frac{a+b}{2}>b$

Prove: If $a,b$ are two distinct real numbers, then either $\frac{a+b}{2}>a$ or $\frac{a+b}{2}>b$ Here is my attempt: Case 1: Multiplying both sides by $2$ and subtracting $b$ gives us: $a>b$. Case 2: Repeating the same argument but now…
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