Mathematics Stack Exchange
Mathematics Stack Exchange

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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Is it bad form to write mysterious proofs without explaining what one intends to do?

Often when doing assignments, I find myself deliberately writing in a "mysterious" way. By this I mean that the reader usually will not understand what exactly is going on and what for, until the very end where all the things come together. A…
Jaood
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how to be good at proving?

I'm starting my Discrete Math class, and I was taught proving techniques such as proof by contradiction, contrapositive proof, proof by construction, direct proof, equivalence proof etc. I know how the proving system works and I can understand the…
uohzxela
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Could I be using proof by contradiction too much?

Lately, I've developed a habit of proving almost everything by contradiction. Even for theorems for which direct proofs are the clear choice, I'd just start by writing "Assume not" then prove it directly, thereby reaching a "contradiction." Is this…
user64844
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6 answers

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 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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Is it okay to reverse engineer proofs in homework questions?

In a linear algebra text book, one homework question I received was: Prove that $\mathbf{a \cdot b} = \frac{1}{4}(\|\mathbf{a + b}\|^2 - \|\mathbf{a - b}\|^2)$. Where $\mathbf{a}$ and $\mathbf{b}$ are vectors in $\Bbb{R}^n$. This is trivial to…
user3002473
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When stating a theorem in textbook, use the word "For all" or "Let"?

(Some report that my question is similar to another post. However, that post is talking about writing the "proof", rather than "stating" the theorem. "Proving" a theorem is NOT of the same structure and situation as "stating" a theorem. So this…
Eric
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Can a proof be just words?

I suppose this is a question about mathematical convention. In a problem in Introduction to Probability by Bertsekas and Tsitsiklis, they ask the reader to prove an identity. But then their proof is mostly words: Problem 3.* Prove the identity $$A…
jds
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What is the correct way of disproving a mathematical statement?

This question is motivated by my midterm exam. In this exam there was a question as follow: Question: If the following statement is true, prove it, otherwise disprove it. If $\mathbf{u}$ and $\mathbf{v}$ are vectors in three dimensions, then …
user155910
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3 answers

Is there a better alternative to the phrase, 'it holds that'?

The following phrases abound in my writing: There exists [whatever] such that [whatever]. For all [whatever] it holds that [whatever]. Lately, I've been feeling that the phrase 'it holds that' is overly long-winded. The only substitute I can think…
goblin GONE
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Prove that $a < b\sqrt{3}$ under conditions given

There are integers $a$ and $b$ such that: 1) $a > b > 1$ 2) $ab+1$ is divisible by $a+b$ and $ab-1$ is divisible by $a-b$. Prove that $a < b\sqrt{3}$. It's really hard, do you see a solution?
applicant
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A proof using the contrapositive

I am trying to prove the following conjecture: Prove that if $m$ and $n$ are integers and $mn$ is even, then $m$ is even or $n$ is even. Proof by contraposition: Assume $m$ and $n$ are odd. Then $m = 2k + 1$ and $n = 2l + 1$. So $$mn = (2k +…
Lee
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Controlled natural language for mathematics

I am a French student very inspired by Bourbaki's but I can no longer stand to write approximate proofs. I was wondering if there was a language between formal and natural language that was both non-binding for the reader (he or she had nothing to…
user601568
8
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1 answer

What can the writer assume in a proof?

When writing a proof, what level of mathematical understanding can I assume my reader has? For example, can I assume they know all odd integers can be represented by $2q+1$? (Right?) Or that all even integers can be represented by $2k$? When do I…
Dennis Hayden
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Proof that $\sqrt{5}$ is irrational

In my textbook the following proof is given for the fact that $\sqrt{5}$ is irrational: $ x = \frac{p}{q}$ and $x^2 = 5$. We choose $p$ and $q$ so that the have no common factors, so we know that $p$ and $q$ aren't both divisible by…
JohnPhteven
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