Questions tagged [proof-writing]

For questions about the formulation of a proof. This tag should not be the only tag for a question and should not be used to ask for a proof of a statement.

Questions with this tag are about the presentation of a mathematical proof. Questions might include:

  • Should I include [x-mathematical detail] at [y-part of this proof]?
  • Is the following a sufficient proof of [x-mathematical tidbit]?
  • I have written the following proof, could I somehow improve it, does it have good flow/can I improve readability?

But this tag is not for asking someone else to write a proof for you, or for how to answer some question. Questions such as: My professor asked me to prove the Pythagorean theorem and I don't know how to begin are not to have this tag.

This tag is intended for use along with other, more "mathematical" tags. A question about the writing of a proof in abstract algebra, for example, should have as well. This tag can be used along with the proof verification tag.

See here for a useful set of guidelines for writing a solution.

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On a long proof

On wikipedia there is a claim that the Abel–Ruffini theorem was nearly proved by Paolo Ruffini, and that his proof spanned over $500$ pages, is this really true? I don't really know much abstract algebra, and I know that the length of a paper will…
Ethan
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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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Systems of linear equations: Why does no one plug back in?

When someone wants to solve a system of linear equations like $$\begin{cases} 2x+y=0 \\ 3x+y=4 \end{cases}\,,$$ they might use this logic: $$\begin{align} \begin{cases} 2x+y=0 \\ 3x+y=4 \end{cases} \iff &\begin{cases} -2x-y=0 \\ 3x+y=4 \end{cases}…
48
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How would one be able to prove mathematically that $1+1 = 2$?

Is it possible to prove that $1+1 = 2$? Or rather, how would one prove this algebraically or mathematically?
amizrahi
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When working proof exercises from a textbook with no solutions manual, how do you know when your proof is sound/acceptable?

When working proof exercises from a textbook with no solutions manual, how do you know when your proof is sound/acceptable? Often times I "feel" as if I can write a proof to an exercise but most of those times I do not feel confident that the…
user46372819
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Level of Rigor in Mathematical Physics

I am a physics/math undergrad and I have recently become familiar with some more rigorous formalisms of mechanics, such as Lagrangian mechanics and Noether's Theorem. However, I've noticed that the writing on mathematical physics (at a level that I…
BusySignal
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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…
46
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Why do we write proofs "forward?"

I am aware that this might turn into a discussion, but I have a feeling this might have an answer (maybe something historical?) instead. I'm hoping that those with speculations keep it in the comments. I have started to work on formal proof writing…
MathMathCookie
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What is the integral of 0?

I am trying to convince my friend that the integral of $0$ is $C$, where $C$ is an arbitrary constant. He can't seem to grasp this concept. Can you guys help me out here? He keeps saying it is $0$.
HowardRoark
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What really is mathematical rigor? How can I be more rigorous?

I'm an undergraduate mathematics student who has received some constructive feedback from two instructors at the end of my exams. Namely, that I am a bit hand-wavey and not always very rigorous. While I greatly appreciate this feedback since I…
A. Thomas Yerger
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Limit of $(1+ x/n)^n$ when $n$ tends to infinity

Does anyone know the exact proof of this limit result? $$\lim_{n\to\infty} \left(1+\frac{x}{n}\right)^n = e^x$$
narendra-choudhary
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The 'Factorialth Root'

I was dealing with the following question, given by my friend: Let $\xi(x)=\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{\cdots}}}}$ Define the series $X$ as $\xi(1),\xi(2),\xi(3),\dots$ Find $n$ for which $\xi(n)$ is the 51st Whole Number in the series. I solved…
DynamoBlaze
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How do I make proofs with long formulae more readable without sacrificing clarity?

Question A lot of things I'm trying to prove just now are turning into "notational hell", which I think makes them very hard to read. I've tried to cut down on this by assuming my reader will understand what definitions are in play, modularising my…
Ten O'Four
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The art of proof summarizing. Are there known rules, or is it a purely common sense matter?

When a proof is long and difficult, it can be really nice vis-à-vis the reader to give a summary or an outline of the deduction before beginning hard work. Are there known rules to give a good proof summary? Are there known rules to find which…
user654868
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7 answers

How to attack "if true, prove it; if not true, give a counterexample" question?

I am taking a basic analysis course. This is a general question that I often encounter in weekly homework. How should we start to attack this type of question: if the statement is true, prove it; if not true, give a counterexample? Yesterday evening…
Q.L.
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