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Questions tagged [proof-verification]

For questions concerning a specific proof or a specific solution, asking for verification, identifying errors, suggestions for improvement, etc. (You should not use this tag if the question does not contain a proposed proof/solution.)

For questions concerning a specific proof (or a proof sketch) or a solution to some problem; asking a question with this tag indicates one would like answers to respond broadly as to the following:

  • Verification of the proof/solution;
  • Identifying errors in the proof/solution;
  • Suggestions for improving the proof/solution;
  • Alternative approaches.

Also, consider the related tags and .

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Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$

I've just started to learn about the tensor product and I want to show: $$(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}.$$ Can you tell me if my proof is right: $\mathbb{Z}/m\mathbb{Z}$…
Rudy the Reindeer
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A very general method for proving inequalities. Too good to be true?

Update I 'repaired' this method, but it changed a lot and I have some different questions, so I posted it separately here. As training for the olympiad, I have to solve a lot of inequalities. Recently, I found a very general method to solve…
Mastrem
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Why do all the Platonic Solids exist?

In three dimensions it is quite easy to prove that there exist at most five Platonic Solids. Each has to have at least three polygons meeting at each vertex, and the angles of these polygons have to add up to less than $2\pi$. This narrows down the…
Oscar Cunningham
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Square root confusion: Why am I getting an answer if it doesn't work?

Alright, so I have $\sqrt{x-15} = 3-\sqrt{x}$. I first square both sides to get $x-15 = (3-\sqrt{x})(3-\sqrt{x})$ which simplifies to $x-15 = 9 -6\sqrt{x} + x$. I solved for $x$ and got $x = 16$, however, when I plug it in, the equation doesn't…
John
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Zero divided by zero must be equal to zero

What is wrong with the following argument (if you don't involve ring theory)? Proposition 1: $\frac{0}{0} = 0$ Proof: Suppose that $\frac{0}{0}$ is not equal to $0$ $\frac{0}{0}$ is not equal to $0 \Rightarrow \frac{0}{0} = x$ , some $x$ not equal…
Lennart
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Proof that every number ≥ $8$ can be represented by a sum of fives and threes.

Can you check if my proof is right? Theorem. $\forall x\geq8, x$ can be represented by $5a + 3b$ where $a,b \in \mathbb{N}$. Base case(s): $x=8 = 3\cdot1 + 5\cdot1 \quad \checkmark\\ x=9 = 3\cdot3 + 5\cdot0 \quad \checkmark\\ x=10 = 3\cdot0 +…
88sandvich
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Find the value of $\sqrt{10\sqrt{10\sqrt{10...}}}$

I found a question that asked to find the limiting value of $$10\sqrt{10\sqrt{10\sqrt{10\sqrt{10\sqrt{...}}}}}$$If you make the substitution $x=10\sqrt{10\sqrt{10\sqrt{10\sqrt{10\sqrt{...}}}}}$ it simplifies to $x=10\sqrt{x}$ which has solutions…
Anthony Muleta
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Where is the flaw in this "proof" of the Collatz Conjecture?

Edit I've highlighted the area in the proof where the mistake was made, for the benefit of anyone stumbling upon this in the future. It's the same mistake, made in two places: This has proven the Collatz Conjecture for all even numbers The Collatz…
stevendesu
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The Chinese Remainder Theorem for Rings.

The Chinese Remainder Theorem for Rings. Let $R$ be a ring and $I$ and $J$ be ideals in $R$ such that $I+J = R$. (a) Show that for any $r$ and $s$ in $R$, the system of equations \begin{align*} x & \equiv r \pmod{I} \\ x & \equiv s…
Ystar
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Is this a new method for finding powers?

Playing with a pencil and paper notebook I noticed the following: $x=1$ $x^3=1$ $x=2$ $x^3=8$ $x=3$ $x^3=27$ $x=4$ $x^3=64$ $64-27 = 37$ $27-8 = 19$ $8-1 = 7$ $19-7=12$ $37-19=18$ $18-12=6$ I noticed a pattern for first 1..10 (in the above…
blue-sky
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Is it a new type of induction? (Infinitesimal induction) Is this even true?

Suppose we want to prove Euler's Formula with induction for all positive real numbers. At first this seems baffling, but an idea struck my mind today. Prove: $$e^{ix}=\cos x+i\sin x \ \ \ \forall \ \ x\geq0$$ For $x=0$, we have $$1=1$$ So the…
Aditya Agarwal
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Lampshade Geometry Problem

Today, I encountered a rather interesting problem in a waiting room: $\qquad \qquad \qquad \qquad$ Notice how the light is being cast on the wall? There is a curve that defines the boundary between light and shadow. In my response below, I will…
Kaj Hansen
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Another proof that dividing by $0$ does not exist -- is it right?

Ok I am in grade 9 and I am maybe too young for this. But I thought about this, why dividing by $0$ is impossible. Dividing by $0$ is possible would mean $1/0$ is possible, which would mean $0$ has a multiplicative inverse. So if we multiply a…
Selim Jean Ellieh
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$\mathbb{R}$ and $\mathbb{R}^2$ isomorphic as groups?

Using the axiom of choice, $\mathbb{R}$ and $\mathbb{R}^2$ are equal-dimensional vector spaces over $\mathbb{Q}$ and so are isomorphic as $\mathbb{Q}$-vector spaces thus as groups. This is obvious, however I recently began reading Godement's…
Maxime Ramzi
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Is this $\gcd(0, 0) = 0$ a wrong belief in mathematics or it is true by convention?

I'm sorry to ask this question but it is important for me to know more about number theory. I'm confused how $0$ is not divided by itself and in Wolfram Alpha $\gcd(0, 0) = 0$ . My question here is: is $\gcd(0, 0) = 0$ a wrong belief in mathematics…
zeraoulia rafik
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