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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.

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Where did I go wrong in this Euler Proof

Why are the two proofs below contradicting each other? $e^{iπ} = -1 $ $e^{π2i}= (e^{iπ})^2 = 1$ $(e^{π2i})^π = 1$ Part 2 $(e^{π2i})^π = e^{{π^2}2i}$ $cos(2{π^2}) = i sin(2{π^2})$ ≠ 1
Yousuf Kanan
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Proof verification for proof by induction for the sum of n natural odd numbers

Suppose we have to prove that $1+3+5+...(2n-1)=n^2$ Here is my "proof," which I did by induction. Since I am learning induction, I wanted to know whether I did it correctly (I don't think I did). For the base case, suppose n=1. Then $2(1)-1=1^2$,…
UserM1
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Prov that: $f^{-1}(G) \subseteq f^{-1}(H)$ whenere $G \subseteq H$

Please verify if this proof is rigorous and correct. And if not provide feedback of what is wrong/lacking. def1 $ A \subseteq B: \Leftrightarrow \forall x \in A \Rightarrow x \in B$ Given a function $f: X \rightarrow Y$, and subsets $A$ of $X$ and…
ALEXANDER
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I don't get the part of the proof where $d'$ can be a common divisor of $a$ and $b$.

This is part of proof in https://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf#page=165 "... show that $d$ is the unique such natural number. To do this, suppose $d'$ is any nautral number with the property the $d$ has: $m$ is a multiple of $d'$…
user665125
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Do we need to consider the cases when both $x$ and $y$ are not irrational?

Suppose there is no rational points on $x^2 + y^2 = c$ where $c $ is a constant. If we plug in $x=0$, then there is no rational solution for $y^2=c$. Thus, $y=\sqrt{c}$ is irrational and we show that $\sqrt{c}$ is irrational. This is the proof I saw…
user665125
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Suppose $a, b \in \mathbb{N}$. If $\frac{a}{b} \notin \mathbb{N}$, then $b>1$.

Suppose $a, b \in \mathbb{N}$. If $\frac{a}{b} \notin \mathbb{N}$, then $b>1$. Is this statement true? I use contrapositive to show that if $b=1$, then $\frac{a}{b}\in\mathbb{N}$ which seems obviously true but I always make obvious mistake so I'm…
user665125
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Proof by induction on a recursive pentagonal number algorithm

I've been tasked to rewrite the following iterative function recursively: int pentagonal(int n) { int result = 0; for (int i = 1; i <= n; i++) result += 3 * i - 2; return result; } Here is my attempt at doing so: // n >= 1 int…
ganondork
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Proof Verification: No $x$ such that $e^x$ = 0

In my school's grade 10 curriculum we learnt something called the natural logarithm. And of course, comes $ln(0) = undefined$. Now of course, every generic math teacher should ask their students, "Why?" Here's my try: $$e^{a + bi} = e^a \times…
MarioPrix
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Find all triples of non-negative

Find all triples of non-negative real numbers $(a,b,c)$ such that: $$\begin{cases}a^2+ab=c \\ b^2+bc=a \\ c^2+ca=b \end{cases}$$ Attempt: $$b= \frac{-c+\sqrt{c^2-4a}}{2}$$ $$2c^2+2ca=-c+\sqrt{c^2-4a}$$ $$2c^2+c(2a+1)=+\sqrt{c^2-4a}$$…
Lambert macuse
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Verifying validity of correctness statement using assertions

I need to verify the validity of this correctness statement by adding any intermediate assertions and inferencing , however I have never seen a statement where the last assertion is the same as the first, so am just a little lost on where to…
algebruh
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Prove the following statements using the indicated method (by contradiction)

I have a problem here hope you will help me. Let a be an integer. If $a^2-3$ is odd then $3a+2$ is even. I am asked to prove this by contradiction. Example: Proposition For all integers $n$, if $n3 + 5$ is odd then n is even. Proof. Let $n$ be any…
Nam do san
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Check proof Dot Product

I want to check my proof of dot product (without using cosine law). We want to prove that $\vec a\cdot \vec b=|\vec a||\vec b|\cos \theta$, where theta is the angle the two vectors form. If we name $\vec a'$ the orthogonal projection of $\vec a$ on…
user10000024
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Proof that $\sqrt{2}$ is irrational, using the prime factorization

I am trying to prove that $\sqrt{2}$ is irrational, assuming the fundamental theorem of arithmetic is true. Here is my attempt. Suppose for the sake of contradiction $\sqrt{2}$ is rational, and write $\sqrt{2} = \frac{a}{b}$ for $a,b \in…
Brad G.
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Finding the magnitude of a function

Find $|X(\omega)|$ where $$ X(\omega)=\frac{1}{1-ae^{i\omega}} $$ Multiplication of the conjugate of the denominator on its numerator and denominator yields $$ X(\omega)=\frac{1-a\cos(\omega)-i\sin(\omega)}{1-2a\cos(\omega)+\omega^2} $$ which…
wd violet
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Alternative proof that $\sqrt{2}$ is irrational

I'm trying to understand an alternative to the standard proof that $\sqrt{2}$ is irrational, which uses the fundamental theorem of arithmetic. It doesn't look overly crisp to me at this moment. Suppose for the sake of contradiction that there…
Brad G.
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