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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.

21426 questions
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Prove $\cos^2(\theta)+\sin^2(\theta) = 1$

$$\cos^2(\theta) + \sin^2(\theta) = 1$$ I solved this by using right triangle, $$\sin(\theta) = \frac{a}{c}, \quad \cos(\theta) = \frac{b}{c}$$ $$\cos^2(\theta) + \sin^2(\theta) = 1$$ $$\Bigl(\frac{b}{c}\Bigr)^2 + \Bigl(\frac{a}{c}\Bigr)^2 = 1…
EM4
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Critique my proof of $f(x) = x^2, x \in \mathbb{R}$ being continuous

Let $\epsilon > 0$ and $a \in \mathbb{R}$. Let $\delta > 0$ s.t $\delta < \frac{\epsilon}{\vert x + a \vert}$ and $\lvert x - a \rvert < \delta$. Thus,  $$\lvert f(x) - f(a) \rvert = \lvert x^2 - a^2 \rvert = \lvert x + a \rvert \lvert x - a \rvert…
Faith Alone
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5
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Can this be considered a formal proof?

I am still learning about mathematical proofs and wanted to ask for some feedback, if possible, of my solution for the following problem. Let $x,y\in \mathbb{Z}$. Prove that $x-y$ is even if and only if $x$ and $y$ are of the same parity. To prove…
Kr'aamkh
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Is this proof of $a^n\times a=a^{n+1}$ correct?

High-schooler here! I am learning logic, and, consequently, I am trying to prove simple things. So I tried to prove $a^{n}\times a=a^{n+1}$: Proof Definitions Definition of exponentiation (D1): ${\displaystyle a^{n}=\underbrace {a \times\cdots…
user784856
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3 answers

Is it true that $\forall x>3, \exists yx$ such that $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1 ?$

Is it true that $\forall x>3, \exists yx$ such that $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1 ?$ Here is my proof but I am stuck in the middle. And I am also wondering if I am on the right track? Let $y = x - a$ for some real…
Jesse Jin
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If $\frac{a}{b}$ is fully reduced, then $a$ is odd or $b$ is odd.

Is the following contrapositive proof correct? Proposition: If $\frac{a}{b}$ is fully reduced, then $a$ is odd or $b$ is odd. Proof: Suppose that $a$ is even and $b$ is even, then $\exists k,\ell \in \mathbb{Z},a = 2k,b=2\ell$, and…
mhdadk
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4 answers

Proof by Contradiction (I think)

Prove: If $x^2+x-6 \ge 0$, then $x\le -3$ or $x \ge 2.$ This is my initial work, but I'm not sure if this is the way to go or if should do a direct proof. Proof by contradiction: Assume $x^2+x-6 \ge 0$ and $-3
Drake
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solution verification| Determine the smallest number that is integer $k$ for which the inequality $x^4+4x^2+k>6x$ is true for every real number x.

the question Determine the smallest number integer $k$ for which the inequality $x^4+4x^2+k>6x$ is true for every real number $x$. my idea $x^4+4x^2-6x+4>4-k => x^4+4x^2-6x+4=(x^2-2x+1)(x^2+2x+4)+3x^2=(x-1)^2((x+1)^2+3)+3x^2 \geq 3$ This means that…
IONELA BUCIU
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Critique my proof that if $x > 0, \exists N \in \mathbb{Z}^{+}$ s.t. $\frac{1}{N} < x < N$.

Pf: Let $x > 0$. By the Archimedean property, $\exists M \in \mathbb{Z}^{+}$ s.t. $\frac{1}{x} < M$. Likewise, $\exists n \in \mathbb{Z}^{+}$ s.t. $x < n$. Let $N = n + M$. Because $n, M > 0 \Rightarrow n + M > 0$ and $(n + M) \in \mathbb{Z}$…
Faith Alone
  • 551
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Is this method of direct proof correct?

My professor in class only did such a proof by contradiction. She would assume $r$ is rational, and contradict this in the end by showing that it cannot be, but I think a direct is cleaner. For my HW, I've done this: Prove: $\sqrt{5 - \sqrt{3}}$ is…
user129393192
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Is my proof of showing "There is an integer $n$ such that $2n^2 - 5n + 2$ is prime" correct?

once again a question on if my proof is correct, since the way it is written differs much with how the book proofs it. I know that the $n$ chosen does not make much of a difference in this case, I am mostly doubting if the steps taken towards the…
Diceble
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2 answers

Munkres Lemma 2.1

I'm trying to make sure that I have correctly proved Munkres' Lemma 2.1, which is left to the reader. The lemma states: Let $f: A \to B$. If there are functions $g: B \to A$ and $h: B \to A$ such that $g(f(a)) = a$ for every $a$ in $A$ and $f(h(b))…
Cardinality
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Alternative proof that the rationals are countable

Does anybody know of proof that the rationals are countable using an array that starts with 1/1 2/1 1/2 3/1 2/3 3/2 1/3 etc. where you generate from p/q the next two fractions to p+q/q and p/p+q Why are all the rationals in the array and…
Luis Shein
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Proving function

I tried to prove $f(n) = 4^n + 5n^2 \log n$ is not $O(2^n ).$ by using contradiction. $4^n + 5n^2 \log n \le C \cdot 2^n$ for $n\ge k$ Then, divide by $2^n$ $2^n \le C - \frac{(5n^2 \cdot \log n)}{2^n}$ for $n\ge k$ but I stuck here. How can I…
user991064
3
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0 answers

If a real number $x$ is rational, then its square is rational

I would like to prove the conditional statement "If a real number $x$ is rational, then its square is rational", and was wondering if this is the correct approach. Let $x$ be a rational, real number, $\frac{a}{b}$, where $a,b\in \mathbb{Z}$ and $b…
zzzzz
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