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.

15776 questions
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Decomposition of a function into positive and negative parts and its integrability

1)Is it true that any function can be decomposed as a difference of its positive and its negative part as $f=f^{+}-f^{-}$ or that function should belong to $\mathcal{L}^{1}(\mathbb{R})$. Also if that function doesn't belong to…
SAMEER
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Proof by contradiction proving both numbers are not odd.

I have to do a proof by contradiction: Suppose $a,b,\in\mathbb{Z}$. If $4| (a^2 + b^2)$ then a and b are not both odd. So far I know that I need to prove that if $4|(a^2+b^2)$ then a and b are both odd. I would use the definition of an odd number…
Wilson
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Proofs involving Well-Defined and One-to-One

Chartrand, 3rd Ed, P224-225: Define a relation $R$ as a relation from A to B. $R$ is well-defined means: $(a,b), (a,c) \in R \implies b = c$. P220: A function $f: A \to B$ is one-to-one means: For all $x, y \in A$, if $f(x) = f(y)$, then $x =…
user53259
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Help proving this Proposition

For every natural number $n$, the integer $6^{2n+1}+8^{3n}$ is divisible by 7. I handled the base case quite well, but got stuck on the induction step. Any help would be greatly appreciated.
user135340
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Are there any proofs that use $0/0$ is indeterminate?

I'd imagine that "$n/0$ is undefined $\forall n\neq 0$" is very useful in finding contradictions, but are there any proofs that somehow use "$0/0$ is indeterminate"?
Hovercouch
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How to write a proof that uses combinatorics?

Imagine you have this trivial problem: How many ways can n people pick two flavours from a choice of k flavours (with no repetition on the flavours). Suppose that you think the answer is ${k \choose 2}^n$ How do you write a formal proof to show…
S0rin
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Help with a proof I came across

I came across this in my textbook and was wondering how it could be proven. If $a\mid m$ and $b\mid m$ and $gcd(a,m) = 1$, then $ab\mid m$. It's near some Euclid and Extended Euclid proofs so I was wondering if it had to do with that.
user135340
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Having Trouble Forming Mathematical Proof

I'm having trouble forming a mathematical proof for a question. I can write down thousands of examples with various values of n that shows it's correct, but I'm not sure how to turn that into a mathematical proof it when multiple functions are…
Yuki
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How can you prove the fundamental theorem of finitely generated abelian groups using the first isomorphism theorem?

I was able to prove the lemma that lets $G$ be a finitely generated abelian group, generated by $n$ elements $\{g_1,g_2,\dotsc,g_n\}$. Then the homomorphism $: \mathbb Z^n \to G$ defined by $(a_1,a_2,\dotsc,a_n) \mapsto g_1^{a_n} g_2^{a_n}$ is an…
user135524
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How to prove that for all natural numbers, $4^n > n^3$?

This is a problem set I have, it's not a homework but it's very important practice... Send me some hints please, I don't want an answer I need to get it by myself but I'm failing miserably... The problem is: Prove that for all natural numbers $n$,…
JOX
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proof by induction - creating summations?

I have two proofs I need to do that I can not figure out how to turn into summations in order to solve. $3|(4^n-1)$ I believe that $|$ is meant to symbolize $3$ divides ... $n!\le n^n$ I have to write it like this $$\sum_{i=1}^{n}i=n$$
Mikky Davey
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Prove that for all $x$ where $01$

Prove that for all $x$ where $0 1.$$ I tried multiple Identities I do not know what I am missing. I have tried changing into different identities.
John Smith
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Wrting equations for work rate problems

Consider the following An experienced bricklayer can work twice as fast as an apprentice bricklayer. After the bricklayers work together on a job for 6 h, the experienced bricklayer quits. The apprentice requires 12 more hours to finish the job.…
Joe Stavitsky
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Need help understanding a specific equality in this proof

Question. Let $f:\mathbb R\to \mathbb R$ be a uniformly continuous function. Show that there exists $a,b>0$ such that $|f(x)|\le a|x|+b,$ $\forall x\in\mathbb R$. Proof. Since $f$ is uniformly continuous, $\forall\epsilon>0$ $\exists\delta>0$,…
homegrown
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Need help with a proof

Let $m, n \in \mathbb{N}$. If $n$ is divisible by $m$, then $m \le n$. So far I have: Let $m,n \in \mathbb{N}$ and assume that $n$ is divisible by $m$. Therefore, there exists $j \in \mathbb{Z}$ such that $n=jm$. By Proposition 2.11 (in the text…
user3182252
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